Reference no: EM132330123
Questions -
Question one - Suppose the distribution of times swum by the women's 100m freestyle competitors at the 12th FINA World Championships in Melbourne, 2007 was normally distributed with a mean μ = 55.70 seconds and a standard deviation σ = 1.60 seconds.
a) Draw and label carefully the distribution of the women's 100 m freestyle competitor times.
b) Use the 68 - 95 - 99.7 % rules to determine the probability that a female swimmer will swim the 100 m in under 52.5 seconds (correct to 3 decimal places)?
c) What is the probability that a swimmer will take longer than 60.5 seconds?
d) Suppose we take a random sample of 16 female 100 m freestyle competitors. Draw the distribution of sample means we might expect if we took repeated samples of size 16 from a population of female 100 m freestyle competitors with mean μ = 55.7 seconds and standard deviation σ = 1.6 seconds.
e) What is the probability of selecting a sample of 16 competitors with a mean time of 54.9 seconds? Do you think this is likely? Why/why not?
Question Two - In order to investigate the flight time between Melbourne and Singapore, a sample of 64 flight times we taken and the sample mean flight time was calculated to be 7.8 hours. The distribution of the flight times is known to be approximately normally distributed with a standard deviation of 0.24 hours.
a) Find a 95% confidence interval for, the mean fight time (correct to 2 decimal places).
b) Interpret your answer from part (a).
c) Suppose that the airline claims that the mean flight time is 7.7 hours. Is the data consistent with this claim? Explain your answer.
d) Calculate a 95% confidence interval for the population of passengers who are likely to rate the in - flight service as "above average" (correct to 2 decimal places).
e) Interpret your answer from (d)
f) A large sample size was taken and another 95% confidence interval was calculated. How would you expect this interval to differ from the interval calculated in (d)?
Question Three - A private investigator claims that he solves 90% of all cases he takes on. A reporter accompanies the investigators on 40 assignments and observes that 33 out the cases are solved. Does this suggest that the investigators claim was exaggerated?
a) What is the value of the sample statistic (correct to 2 decimal places)?
b) If we conducted and hypothesis test express the research hypothesis in words.
c) Express the null and alternative hypothesis (using appropriate symbols) for the hypothesis test identified above.
d) Are the results of this research significant (testing at the 5% level of significance)? Why/why not?
e) What would the conclusion be in response to the research hypothesis?
Question Four - The green life electric light bulb company claims to produce energy efficient light bulbs that last on average 740 hours. An independent tester tests a random sample of 10 light bulbs and records the results below:
|
Bulb
|
Hours of life
|
|
1
|
738
|
|
2
|
716
|
|
3
|
745
|
|
4
|
767
|
|
5
|
705
|
|
6
|
734
|
|
7
|
718
|
|
8
|
717
|
|
9
|
721
|
|
10
|
730
|
Does the data provide sufficient evidence that the average energy efficient light bulb life differs from 740? Test at the 5% level of significance. Set out your solution using the following steps-
a) Write the research hypothesis in words.
b) Formulate null and alternative hypothesis (using appropriate symbols) to test if the average bulb life differs from 740.
c) What is the value of the test statistic?
d) What is the p - value?
e) What would be the conclusion in the above example if the level of significance is 5%?
f) Interpret a 95% confidence interval for the average life of the energy efficient bulbs (correct to 2 decimal places).
g) Is the confidence interval calculated in (f) consistent with the conclusion reached in (e)? Explain your reasoning.
Question five - Researchers were interested in whether state wide water saving advertising campaign was successful. A sample of 50 homes had their water usage recorded before and after the campaign.
The average water usage before the campaign was found to be 493 liters per day. After the campaign the average water usage was 425 liters per day. Do the results suggest the campaign was successful?
a) Is the data paired or independent?
b) Do the plots above suggest it is appropriate to use the t- distribution for this data? Explain your answer.
c) Write a report on the results of the hypothesis test.
Question six - Do smarter people earn more money? A sample of 100 employees was taken and their IQ scores and weekly earnings recorded.
a) If we conducted an hypothesis test, express the research hypothesis in words.
b) Assuming the sample of employees has been drawn at random from a much larger population of employees, can we conclude there is a relationship between IQ scores and weekly income? Write your results in a report format.