Use the given frequency distribution to construct a

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question. Make sure CLARIFY/JUSTIFYyour answers with concise phrase or word. You can use MINITAB but need to write down necessary steps and intermediate results.

 

 

1)  Use the given frequency distribution to construct a frequency histogram, and a relative frequency histogram.

 

Height (in inches)

               

 

 

2) Use the histogram below to approximate the mode heart rate of adults in the gym.

 

                 

               

 

 

3) The heights (in inches) of all 10 adult males in an office are listed below. Find the population standard deviation and the sample standard deviation

 

               

 

 

4) A random sample of n = 12 observations is selected from a normal population to test H0: μ = 22.1 against Ha: μ> 22.1 at α = .05. Specify the rejection region.       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5) A recipe submitted to a magazine by one of its subscribers states that the mean baking time for a cheesecake is 55 minutes. A test kitchen preparing the recipe before it is published in the magazine makes the cheesecake 10 times at different times of the day in different ovens. The following baking times (in minutes) are observed.

 

54           55           58           59           59           60           61           61           62           65

 

Assume that the baking times belong to a normal population. Test the null hypothesis that the mean baking time is 55 minutes against the alternative hypothesis  μ> 55. Use α = .05.            

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6) In order to compare the means of two populations, independent random samples of 225 observations are selected from each population with the following results.

 

Sample 1              Sample 2

 1 = 478 2 = 481

s1 = 14.2               s2 = 11.2

 

Test the null hypothesis H0: (μ1 - μ2) = 0 against the alternative hypothesis   using  Give the significance level, and interpret the result.       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7) Independent random samples selected from two normal populations produced the following sample means and standard deviations.

 

Sample 1              Sample 2

  = 14        = 11

 1 = 7.1  2 = 8.4

s1 = 2.3 s2 = 2.9

 

Conduct the test  : (  -  ) = 0 against.  : ( -  ) ≠ 0,  Use α = .05.         

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8) Independent random samples from normal populations produced the results shown below.

 

Sample 1: 5.8, 5.1, 3.9, 4.5, 5.4

Sample 2: 4.4, 6.1, 5.2, 5.7

 

a.            Calculate the pooled estimator of σ2.

b.            Test μ1<μ2 using α = .10.

c.             Find a 90% confidence interval for (μ1 - μ2).       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9) A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let   be the true mean weight of individuals before starting the diet and let   be the true mean weight of individuals after 3 weeks on the diet.

 

 

 

Summary information is as follows:   = 5,   = 1.58.

 

Test to determine if the diet is effective at reducing weight. Use α = .10.             

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10) The scores on a standardized test are reported by the testing agency to have a mean of 75. Based on his personal observations, a school guidance counselor believes the mean score is much higher. He collects the following scores from a sample of 50 randomly chosen students who took the test.

 

39           48           55           63           66           68           68           69           70           71

71           71           73           74           76           76           76           77           78           79

79           79           79           80           80           82           83           83           83           85          

85           86           86           88           88           88           88           89           89           89          

90           91           92           92           93           95           96           97           97           99

 

Find and interpret the p-value for the test of H0: μ = 75 against Ha: μ> 75.            

 

 

 

 

 

 

 

 

 

 

 

 

11) A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 70 hours. In order to test whether the time to fill out the form has been reduced, a sample of 94 small business owners who annually complete the form was randomly chosen and their completion times recorded. The mean completion time for the sample was 69.6 hours with a standard deviation of 23 hours. State the rejection region for the desired test at