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From past experience, a server at a restaurant knows that her tips follow a right-skewed distribution with mean $6 and standard deviation $4.
What is the probability that the servers next 30 tips have a mean between $6 and $7? (Assume that these 30 customers represent a simple random sample).
If the server has 40 customers in one shift, what is the probability that her total tips are less than $250? (Assume that these 40 customers represent a simple random sample).
Suppose you roll a standard die 2000 times and let X be the sum of the values you get. Using the Central Limit Theorem, for what value of a is P[X >= a] approximately equal to P[N(0,1) >= 2] ?
An instructor claims the average time to take a statistics test is greater than 39 min. As, if a sample of 33 students took 43 min. is the instructor's claim true?
An aptitude test has a mean of 220 and standard deviation of 10. find the corresponding z score for:
A bag contains 5 blue balls and 8 purple balls. If 3 balls are chosen randomly and without replacement, form the bag. Let x be the number of blue balls obtained. Then x has a distribution.
In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Write the null hypothesis tested by the ANOVA.
A company auditor was interested in estimating the total number of travel vouchers that were incorrectly filed. In a SRS of size n =50 oft of the group of N = 250, were filed incorrectly.
They have collected data on gender, shoe size, and height to see if they can change their business model to include only one size of shoes regardless height or gender of the wearer.
A researcher tested the reading ability of two groups of primary care patients. The scores on the test range from 1 to 9 with 9 indicating a high degree of reading ability and 1 very limited reading ability.
If these answers were combined into single statistic, how could we explain sample space? Mention how many elements are in sample space?
Can we conclude at the 5% significance level that the population mean weight of athletic men is lower than the population mean weight of non-athletic men?
Let X1, ..., Xn be a random sample from a two-parameter exponential distribution, Xi ~ EXP (theta, eta). (a) Assuming it is known that eta = 150, find a pivotal quantity for the parameter theta based on the sufficient statistic.
40 were in favor of the Independent candidate, and 140 were undecided. At a 1% level of significance, test to see if the proportion of voters has changed. Calculate the value of the Chi-Square Test Statistic for this problem. What is it?
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