Statistics

  1. In a study of pain relievers, 25 people were given product A, and all but 7 experienced relief.  In the same study,  50 people were given product B, and all but 8 experienced relief.    Fill in the blanks of the statement below to make the statement the most reasonable possible.

 

Product __________performed better in the study because only ____% failed to get relief with this product, whereas ____% failed to get relief with Product ______.

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  1. Use the calculator provided to solve the following problems.

 

  1. Consider a t distribution with 26 degrees of freedom . Compute P(-1.87 < t < 1.87) Round your answer to at least three decimal places.
  2. Consider a t distribution with 21 degrees of freedom.  Find the value of c such that P (t ≥ c) = 0.05.  Round our answer to at least three decimal places.

 

P ( -1.87 < t < 1.87 ) =

C =

 

 

 

 

  1. Suppose that we want to estimate the mean germination time of strawberry seeds. The germination times for the sample of strawberries we choose has a mean of 18 days and a standard deviation of 1.5 days.  For each of the following samplings scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.

 

( In the table Z refers to a variable having a standard normal distribution, and t refers to a variable having a t distribution)

Sampling Scenario Z t Could use either Z or t unclear
1.       The sample has size 19, and it is from a normally distributed population with unknown standard deviation        
2.        The sample has size 95, and it is from non-normally distributed population with a known standard deviation of 1.2.        
3.        The sample has size 85, and it is from a non-normally distributed population.        
4.        The sample has size 17, and it is from a population with a distribution about which we know very little        
5.        The sample has size 13, and it is from a normally distributed population with a known standard deviation of 1.2.        

 

  1. The standard deviation of test scores on a certain achievement test is 11. A random sample of 80 scores on this test had a mean of 70.4.  Based on this sample find a 90% confidence interval for the true mean of all scores.  Than complete the table below .

Carry your intermediate computations to at least three decimal places.  Round your answers to one decimal place.

  1. What is the lower limit of the 90% confidence interval?
  2. What is the upper limit of the 90% confidence interval ?

 

  1. Suppose that a random sample of 16 adults U.S. males has a mean height of 71 inches with a standard deviation of 2.9 inches.  If we assume that the heights of adult males in the U.S.  are normally distributed, find a 95% confidence interval for the mean height of all U.S. males.  Then complete the table below

 

Carry your intermediate computations to at least three decimals places. Round your answer to one decimal place (If necessary, consult a list of formulas).

  1. What is the lower limit of the confidence interval?
  2. What is the upper limit of the confidence interval?

 

  1. Suppose that 192 out of random sample of 275 letters mailed in the United States were delivered the day after they were mailed. Based on this, compute a 95% confidence interval for the proportion of all letters mailed in the United States that were delivered the day after they were mailed.  Then complete the table below

 

Carry your intermediate computations to at least three decimal places.  Round your answers to one decimal place.

  1. What is the lower limit of the 95% confidence interval?
  2. What is the upper limit of the 95% confidence interval ?

 

  1. A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to estimate the mean monthly mileage, µ, of cars rented in the U.S. over the past year.  The consumer group plans to choose a random sample of monthly U.S. rental car mileages and then estimate µ, using the mean of the sample.

 

Using the value 800 miles per month as the standard deviation of monthly U.S. rental care mileages from the past year, what is the minimum sample size needed in order for the consumer group to be 99% confident that its estimate is within 175 miles per month of µ?

 

Carry your intermediate computations to at least three decimals places.  Write the answer as a whole number( and make sure that it is the minimum whole number that satisfies the requirements).

 

Answers:

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