Reference no: EM131238172

Question 1
Page 505 Ex 77

An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees.

Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2 and then perform a hypothesis at a 1% significance level using the Critical Value procedure.

What is the null and alternate hypothesis for this hypothesis test?

a Ho: μ = 4.5, Ha: μ > 5.1
b Ho: μ = 4.5, Ha: μ < 5.1
c Ho: μ = 4.5, Ha: μ > 4.5
d Ho: μ = 4.5, Ha: μ < 4.5
________

What is the numerical value of α for this test?

Enter answer as a 2 place decimal with a 0 to the left of the decimal point.

Do not enter answer as a percent.
________

What is the appropriate distribution for performing this test?

a z distribution
b t distribution
c Either distribution
d Neither. This question does not depend on knowing the appropriate distribution.

Select and enter the appropriate letter
________

What is the critical value for the test statistic?

Enter answer as a 3 place decimal rounded to 3 decimal places.
________

What is the numerical value of the test statistic?

Enter answer as a decimal rounded to 1 decimal place.
________

Based upon the Hypothesis test what is your decision?

a There is insufficient evidence, based upon the data, to accept the alternate hypothesis.
b There is sufficient evidence, based upon the data, to accept the alternate hypothesis.
c It is not possible to make a decision (null or alternate), based upon the data.
d A strong case could be made for either decision (null or alternate) based upon the data.
________

Question 2

Page 505 Ex 77

An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees.

Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2 and then perform a hypothesis at a 1% significance level using the Pvalueprocedure.l.

What is the null and alternate hypothesis for this hypothesis test?

a Ho: μ = 4.5, Ha: μ > 5.1
b Ho: μ = 4.5, Ha: μ < 5.1
c Ho: μ = 4.5, Ha: μ > 4.5
d Ho: μ = 4.5, Ha: μ < 4.5
________

What is the numerical value of α for this test?
Enter answer as a 2 place decimal with a 0 to the left of the decimal point.
Do not enter answer as a percent.
________

What is the appropriate distribution for performing this test?
a z distribution
b t distribution
c Either distribution
d Neither. This question does not depend on knowing the appropriate distribution.
Select and enter the appropriate letter
________

What is the numerical value of the test statistic?
Enter answer as a decimal rounded to 1 decimal place.
________

What is the numerical value of the Pvalue?
Enter answer rounded to 2 decimal places with a zero to the left of the decimal point.
________

What is the Pvalue Decision Rule?
a. The data supports the alternate hypothesis if the Pvalue is greater than the significant level of the test.
b. The data supports the alternate hypothesis if the Pvalue is less than the significant level of the test.
c. The Pvalue must equal the significant level of the test for the decision of the hypothesis test to be alternate.
d. The Pvalue must not be equal the significant level of the test for the decision of the hypothesis test to be alternate.
Select the correct answer and enter the appropriate letter.
________

Based upon the Hypothesis test what is your decision?
a There is insufficient evidence, based upon the data, to accept the alternate hypothesis.
b There is sufficient evidence, based upon the data, to accept the alternate hypothesis.
c It is not possible to make a decision (null or alternate), based upon the data.
d A strong case could be made for either decision (null or alternate) based upon the data.
________

Question 3

Page 505 Ex 75 (Classical procedure)

From Generation to Generation, the mean age when smokers first start to smoke varies. However, the standard deviation of the age remains constant of around 2.1 years. A survey of 40 smokers of this generation was done to see if the mean starting age is less than 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at a 5% level?

Note:

The null hypothesis must include an equal sign. The alternate hypothesis must not include an equal sign.

When the population standard deviation is given (2.1) and the sample standard deviation is also given (1.3) we always use the population standard deviation.

What is the Null Hypothesis?
a The mean age of first starting to smoke is less than or equal to (< = ) 18.1
b The mean age of first starting to smoke is greater than or equal to (> =) 18.1
c The mean age of first starting to smoke is not equal to (≠) 19
d The mean age of first starting to smoke is greater than or equal to(> =) 19
e The mean age of first starting to smoke is less than or equal to (< =) 19
Enter the correct answer by selecting the appropriate letter without a decimal point.
________

What is the Alternate Hypothesis?
Note; The alternate hypothesis must not include an equal sign. It may include a not equal sign.
a The mean age of first starting to smoke is less than (< ) 18.1
b The mean age of first starting to smoke is greater than (>) 18.1
c The mean age of first starting to smoke is not equal to (≠) 19
d The mean age of first starting to smoke is greater than (> ) 19
e The mean age of first starting to smoke is less than (< ) 19
f The mean age of first starting to smoke is not equal to (≠) 19
Enter the correct answer by selecting the appropriate letter without a decimal point.
________

What is the significance level of the test?
Enter answer as a 2 place decimal with a 0 entered to the left of the decimal point.
Do not enter answer as a percent.
________

What is the appropriate distribution to use to answer the question?
a Uniform Distribution
b Normal Distribution
c t Distribution
d Chi Square Distribution
e F Distribution

Enter the correct answer by selecting the appropriate letter without a decimal point.
________

What is the critical value of the Test Statistic?
Enter answer as a 2 or 3 place decimal.
________

What is the numerical value of the Test Statistic?
Enter answer with 2 place precision.
________

What is the Decision rule?
The decision is the Alternate Hypothesis if the Test Statistic is:
a Greater than or equal to the Critical Value. (Equal to or more positive than the critical value.)
b Smaller than or equal to the Critical Value. (Equal to or more negative than the critical value.)
c Not equal to the Critical Value. (Greater than or less than the critical value.)
Enter the correct answer by selecting the appropriate letter without a decimal point.
________

What is the appropriate decision based upon your analyses of the data
a There is sufficient evidence reject the null hypothesis.
b There is insufficient evidence to reject the null hypothesis.
c There is insufficient evidence to make a decision based upon the data.
Enter the correct answer by selecting the appropriate letter without a decimal point.
________

Question 4
Page 505 Ex 75 (Pvalue procedure)
From Generation to Generation, the mean age when smokers first start to smoke varies. However, the standard deviation of the age remains constant of around 2.1 years. A survey of 40 smokers of this generation was done to see if the mean starting age is less than 19. The sample mean was 18.1. Do the data support the claim at a 5% level?
Note: The null hypothesis must include an equal sign. The alternate hypothesis must not include an equal sign.
What is the Null Hypothesis?
a The mean age of first starting to smoke is less than or equal to (< = ) 18.1
b The mean age of first starting to smoke is greater than or equal to (> =) 18.1
c The mean age of first starting to smoke is not equal to (≠) 19
d The mean age of first starting to smoke is greater than or equal to(> =) 19
e The mean age of first starting to smoke is less than or equal to (< =) 19
Enter the correct answer by selecting the appropriate letter without a decimal point.
________

What is the Alternate Hypothesis?
a The mean age of first starting to smoke is less than (< ) 18.1
b The mean age of first starting to smoke is greater than (>) 18.1
c The mean age of first starting to smoke is not equal to (≠) 19
d The mean age of first starting to smoke is greater than (> ) 19
e The mean age of first starting to smoke is less than (< ) 19
f The mean age of first starting to smoke is equal to (≠) 19
Enter the correct answer by selecting the appropriate letter without a decimal point.
________

What is the significance level of the test?
Enter answer as a 2 place decimal with a 0 entered to the left of the decimal point.
Do not enter answer as a percent.
________

What is the appropriate distribution to use to answer the question?
a Uniform Distribution
b Normal Distribution
c t Distribution
d Chi Square Distribution
e F Distribution

Enter the correct answer by selecting the appropriate letter without a decimal point.
________

What is the numerical value of the Test Statistic?
Enter answer rounded to 2 decimal places.
________
What is the numerical value of the Pvalue?
Enter answer rounded to 3 or 4 place places with a zero to the left of the decimal place.
Do not enter answer as a percent.
________

What is the Pvalue Decision Rule?
a. The data supports the alternate hypothesis if the Pvalue is greater than the significant level of the test.
b. The data supports the alternate hypothesis if the Pvalue is less than or equal to the significant level of the test.
c. The Pvalue must equal the significant level of the test for the decision of the hypothesis test to be alternate.
d. The Pvalue must not be equal the significant level of the test for the decision of the hypothesis test to be alternate.
Enter the correct answer by selecting the appropriate letter without a decimal point.
________

What is the appropriate decision based upon your analyses of the data?
Enter the correct answer by selecting the appropriate letter without a decimal point.
a There is sufficient evidence reject the null hypothesis.
b There is insufficient evidence to reject the null hypothesis.
c There is insufficient evidence to make a decision based upon the data.
Enter the correct answer by selecting the appropriate letter without a decimal point.
________

Question 5
I Page 505 Ex 80 (Problem and Data Modified)
Your statistics instructor claims that 60% of students that take her Elementary Statistics class go through life feeling more enriched. You believe the actual number of students that took her Elementary Statistics class that feel more enriched is less than 60%. You decide to check her conjecture by randomly survey 64 of her past students. In your random survey of 64 of her previous students 33 of the students felt more enriched. At a significance level of 5% does the data support your belief?
What is the null hypothesis for this hypothesis test?
a The number of students that took her class and feel more enriched is less than or equal to 60%.
b The number of students that took her class and feel more enriched is less than 60%.
c The number of students that took her class and feel more enriched is more than or equal to 60%
d The number of students that took her class and feel more enriched is more than 60%.
e The number of students that took her class and feel more enriched is not equal to 60%.
Enter the correct answer by selecting the appropriate letter without a decimal point.
________

What is the alternate hypothesis for this hypothesis test?
a The number of students that took her class and feel more enriched is less than or equal to 60%.
b The number of students that took her class and feel more enriched is less than 60%.
c The number of students that took her class and feel more enriched is more than or equal to 60%
d The number of students that took her class and feel more enriched is more than 60%.
e The number of students that took her class and feel more enriched is not equal to 60%.
Enter the correct answer by selecting the appropriate letter without a decimal point.
________

What is the significance level of the test?
Enter answer as a 2 place decimal with a 0 entered to the left of the decimal point.
Do not enter answer as a percent.
________

What is the appropriate distribution to use to answer the question?
a Uniform Distribution
b Normal Distribution
c t Distribution
d Chi Square Distribution
e F Distribution

Enter the correct answer by selecting the appropriate letter without a decimal point.
________

What is the numerical value of the Test Statistic?
Enter answer as a decimal rounded to 2 places.
________

What is the numerical value of the Pvalue?
Enter answer rounded to 3 places with a zero to the left of the decimal place.
Do not enter answer as a percent.
________

What is the Pvalue Decision Rule?
a. The data supports the alternate hypothesis if the Pvalue is greater than the significant level of the test.
b. The data supports the alternate hypothesis if the Pvalue is less than or equal to the significant level of the test.
c. The data supports the alternate hypothesis if the Pvalue equals the significant level of the test.
d. The data supports the alternate hypothesis if the Pvalue does not equal the significant level of the test.
Select the correct answer and enter the appropriate letter without a decimal point.
________

What is the appropriate decision based upon your analyses of the data?
Enter the correct answer by selecting the appropriate letter without a decimal point.
a There is sufficient evidence reject the null hypothesis.
b There is insufficient evidence to reject the null hypothesis.
c There is insufficient evidence to make a decision based upon the data.
Enter the correct answer by selecting the appropriate letter without a decimal point.
________
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Question 10
A survey of American Society of Investors found 30% of individual investors have used a discount broker.
In a random sample of nine individuals, what is the probability that:

a. Exactly two of the sample individuals have used a discount broker? P(x = 2)
Enter answer rounded to 3 or 4 decimal places with 0 to the left of the decimal point.
________

b. None of the 9 individuals have used a discount broker. P(X = 0)
Enter answer rounded to 3 or 4 decimal places with a 0 to the left of the decimal point.
________

c. Two or three individuals have used a discount broker. P( 2<= X <= 3)
Enter answer rounded to 3 or 4 decimal places with a 0 to the left of the decimal point.
________

d. What is the mean and standard deviation for this distribution?
Enter each answer rounded to 2 decimal places in the order in which the question was asked.
________

Question 2

A.C. Nielsen Company provides information to organizations advertising on television. Prior research indicates that adult Americans watch an average of 6.0 hours of television per day with a standard deviation of 1.5 hours.

Assuming the time distribution is normally distributed:

What is the probability that a randomly selected adult Americans watches 5 or more hours of television per day?
Enter answer rounded to 3 or 4 decimal places with a 0 to the left of the decimal point. Do not enter answer as a percent.
________

What is the probability that a randomly selected adult Americans watches between 7 and 8 hours (inclusive) of television per day?
Enter answer rounded to 3 or 4 decimal places with a 0 to the left of the decimal point. Do not enter answer as a percent.
________

For how many hours per day must an adult American watch television in order to be in the top 5% of all the adult Americantelevision watchers?
Enter answer rounded to 1 decimal place.
________

In a sample of 25 randomly selected adult Americans what is the probability that the average time for watching television per day will be equal to or exceeds 6.5 hours?
Enter answer rounded to 3 decimal places with a 0 to the left of the decimal point. Do not enter answer as a percent.
________

Question 3

The owner of the Britten's Egg Farm wants to estimate the mean number of eggs produced per chicken. A representative random sample of 20 chickens show they produce an average of 25 eggs per month with a sample standard deviation (s) of 2 eggs per month. The distribution is known to be symmetrical and is close enough to normal to be treated as a normal distribution.

Answer the following questions related to the above paragraph and then calculate a 90% confidence interval for the mean number of eggs produced per chicken on the Britten's Egg Farm.

What is the point estimate of the mean number of eggs produced per chicken?
Enter answer with 0 decimal places (integer).
________

What is the appropriate distribution for calculating a 90% confidence interval?
a Uniform distribution
b Normal distribution
c t distribution
d Chi Square distribution
Answer this question by entering the appropriate letter.
________

What is the degrees of freedom (dF) for the appropriate distribution. Enter Na if dF is not required by the appropriate distribution.
________

Calculate the margin of error for the 90% confidence interval for the mean amount of eggs laid per month on the Britten's Egg Farm.
Enter answer rounded to 1 decimal point. Include a zero to the left of the decimal point if the margin of error is a number between -1 and +1.
________

The 90% conference interval for the mean number eggs produced per month is:
Enter the lower and upper limits for the conference interval by entering the lower limit first.
Rounded each conference limit to 1 decimal point.
________

Prior to this study the owner of the Britten's Egg Farm Egg Farm believed the mean amount off eggs produced per month on his farm was 30.

Does the study support his belief with a 90% confidence?

a Yes. The mean amount of eggs produced per month on his farm could be 30 per month because the number 30 is not contained in the confidence interval.

b Yes. The mean amount of eggs produced per month on his farm could be 30 per month because the number 30 is contained in the confidence interval.

c No. The mean amount of eggs produced per month on his farm is most likely not 30 per month because the number 30 is not contained in the confidence interval.

d No. The mean amount of eggs produced per month on his farm is most likely not 30 per month because the number 30 is contained in the confidence interval.

e The owner cannot comment on the mean amount of eggs produced per month on his farm because the confidence interval is based upon a sample.
Enter the correct answer by selecting and entering the appropriate letter.
________

Question 4

The waiting time for customers at MacBerger Restaurants follows a normal distribution with a population standard deviation of 1 minute.At the Warren Road MacBerger, the quality assurance department sampled 49 customers and found that the mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes.

The Null Hypothesis is:

a The waiting time for customers at MacBerger Restaurants is equal to _______.

b The waiting time for customers at MacBerger Restaurants is greater than _______.

c The waiting time for customers at MacBerger Restaurants is less than _______.

d The waiting time for customers at MacBerger Restaurants is not equal to _______.

Enter the correct answer by selecting the appropriate letter and then entering the correct number. Enter number to the same precision as presented in the question.
________

The Alternate Hypothesis is:
a The waiting time for customers at MacBerger Restaurants is equal to
______.

b The waiting time for customers at MacBerger Restaurants is greater than
______.

c The waiting time for customers at MacBerger Restaurants is less than
______.

d The waiting time for customers at MacBerger Restaurants is not equal to
______.

Enter the correct answer by selecting the appropriate letter and then entering the correct number. Enter number to the same precision as presented in the question.
________

The appropriate distribution is:
a Uniform Distribution
b Normal Distribution
c t Distribution
d Chi Square Distribution

The Hypothesis test is a:
a Left tail test
b Right tail test
c Two tail test

Enter the appropriate letters for answering the questions in the same order in which the questions are asked.
________

Select and enter the letter for the appropriate decision rule.
Enter the critical value as a decimal rounded to 2 or 3 places.

Decision:

a Ha hypothesis: If the test statistic is equal to or greater than the critical value which is _____.
b Ha hypothesis: If the test statistic is equal to or less than the critical value which is _____.
c Ha hypothesis: If the absolute value of the test statistic is equal to or greater than the critical value which is _____.
________

The numerical value of the test statistic is:
Enter answer rounded to 2 decimal places.
________

Hypothesis Test Decision:

a Null Hypothesis: Do not reject the null hypothesis. The data does not support the Alternate Hypothesis.

b Alternate Hypothesis: Reject the null hypothesis. The data supports the Alternate Hypothesis.

c The waiting time for customers at MacBerger Restaurants cannot be determined because the data set is a sample.

Enter the correct answer by selecting the appropriate letter.
________

An alternate method for performing the Hypothesis Test would be to calculate a Pvalue based upon the numerical value of the Test Statistic.
If the Pvalue is larger than the significance level of the test the appropriate decision, based upon the numerical value of the test statistic, would be the Null Hypothesis. If the Pvalue is less than or equal to the significance level of the test the appropriate decision, based upon the numerical value of the test statistic, would be the Alternate Hypothesis.

Based upon the data what is the Pvalue for the Hypothesis Test?

Enter answer as a decimal rounded to 2 places with a zero to the left of the decimal point.

Do not enter answer as a percent.
________

Question 5. Some of the following statements refer to the null hypothesis, some to the alternate hypothesis.State the null hypothesis, H0, and the alternative hypothesis. Ha, in terms of the appropriate parameter (μ or p).

a. The mean number of years Americans work before retiring is 34.
b. At most 60% of Americans vote in presidential elections.
c. The mean starting salary for San Jose State University graduates is at least $100,000 per year.
d. Twenty-nine percent of high school seniors get drunk each month.
e. Fewer than 5% of adults ride the bus to work in Los Angeles.
f. The mean number of cars a person owns in her lifetime is not more than ten.
g. About half of Americans prefer to live away from cities, given the choice.
h. Europeans have a mean paid vacation each year of six weeks.
i. The chance of developing breast cancer is under 11% for women.
j. Private universities' mean tuition cost is more than $20,000 per year.

FOR THE BEOW QUESTIONS ANSWER THE FOLLOWING:

a. H0: _______
b. Ha: _______
c. In words, CLEARLY state what your random variable X ¯ or P′ represents.
d. State the distribution to use for the test.
e. What is the test statistic?
f. What is the p-value? In one or two complete sentences, explain what the p-value means for this problem.
g. Use the previous information to sketch a picture of this situation. CLEARLY, label and scale the horizontal axis and shade the region(s) corresponding to the p-value. Figure E1 h. Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

i. Alpha: _______
ii. Decision: _______
iii. Reason for decision: _______
iv. Conclusion: _______
i. Construct a 95% confidence interval for the true mean or proportion. Include a sketch of the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval.

Note:

The Null Hypothesis always includes the equal sign and the Alternate Hypothesis never includes an equal sign.

Data given in a question is never part of Null and/or Alternate Hypothesis.

Does the expression "at least" includes the equal sign?

Does the expression "at most" includes the equal sign?

When a question includes a population and a sample standard deviation the population standard deviation is the appropriate standard deviation to use for performing the analysis.

Question 6. Toastmasters International cites a report by Gallop Poll that 40% of Americans fear public speaking. A student believes that less than 40% of students at her school fear public speaking. She randomly surveys 361 schoolmates and finds that 135 report they fear public speaking. Conduct a hypothesis test to determine if the percent at her school is less than 40%.

Question 7. Registered nurses earned an average annual salary of $69,110. For that same year, a survey was conducted of 41 California registered nurses to determine if the annual salary is higher than $69,110 for California nurses. The sample average was $71,121 with a sample standard deviation of $7,489. Conduct a hypothesis test.

Question 8. A recent survey in the N.Y. Times Almanac indicated that 48.8% of families own stock. A broker wanted to determine if this survey could be valid. He surveyed a random sample of 250 families and found that 142 owned some type of stock. At the 0.05 significance level, can the survey be considered to be accurate?

Question 9. The student academic group on a college campus claims that freshman students study at least 2.5 hours per day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of 30 freshman students and found a mean study time of 137 minutes with a standard deviation of 45 minutes. At α = 0.01 level, is the student academic group's claim correct?