The Revenue Commissioners in Ireland conducted a contest for promotion. Statistics from the ages of successful and unsuccessful applications are given below. Some of the unsuccessful applicants charged that the competition involved discrimination based on age. Assume the data were normally distributed.  Sample size Sample mean Sample standard deviation Ages of unsuccessful applicants 26 47 7.2 Ages of successful applicants  30 43.9 5.9 Construct a 95% confidence interval for the difference between the mean age of the successful applicants and the unsuccessful applicants. Show detailed work for the following steps: (6pts)  a) Calculator command:  b) Information input:  c) Confidence interval (round to 1 decimal place):  d) Interpretation:   

Find the indicated probability. Round the answer to 4 decimal places. (3pts) You are dealt two cards successively without replacement from a shuffled deck of 52 playing cards. Find the probability that both cards are black.    

A cereal company claims that the mean weight of the cereal in its packets is 14 oz. The weights (in ounces) for the cereal in a random sample of 8 of its cereal packets are listed below. 14.6       13.8        14.1     13.7       14.0      14.4      13.6       14.2   Assume the sample comes from a normal distribution population. Test the claim at the 0.01 significance level. (14pts) Round the sample mean and the sample standard deviation to 2 decimal places. Perform the following steps:  (3pts) Step 1: Requirements (2pts) Step 2:                 (3pts) Step 3: Test statistic (round to 3 decimals) (3pts) Step 4: p- value (round to 4 decimals) (2pts) Step 5: P- value Method  (1pt) Step 6: Conclusion  

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution.A sociologist develops a test to measure attitudes towards public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 94% confidence interval for the mean score of all such subjects using a calculator command. Make sure to include correct symbol, formula and round off rule for each step. (12pts)  (2pts) Point estimate (sample mean)  (3pts) Critical value ( Round to 3 decimal places)(3pts) Margin of Error (Round to 1 decimal place)(3pts) CI (Round to 1 decimal place)(1pt) Interpretation:

Find the indicated probability. (4pts)The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women. Among the last 12 participants there have been only 4 women. If participants are picked randomly, what is the probability of getting 4 or fewer women when 12 people are picked? Make sure to first define variable X, then calculate the probability Define variable X=

Two types of flares are tested and their burning times (in minutes) are recorded. The summary statistics are given below.Brand X                                   Brand Yn = 45                                      n = 50 x-bar = 20.4 min                     x-bar = 16.1 mins = 1.5 min                               s = 0.9 min A) Use a 0.05 significance level to test the claim that the two samples are from populations with the different means. (14pts) Perform the following steps: (3pts) Step 1: Requirements (2pts) Step 2:                 (3pts) Step 3: Test statistic: (round to 3 decimal places) (3pts) Step 4: Critical value (round to 3 decimal places) (2pts) Step 5: Critical value method  (1pt) Step 6: Conclusion    B) Construct a 95% confidence interval for the difference between the burning mean times of two types of flares using the following steps. (6pts) Perform the following steps:             (1pt) Command:              (2pts) Information for the command:             (1pt) CI: (round to 1 decimal place)             (2pts) Does it appear there is a difference between the two mean times of two types of flares? Explain   C) (2pts) Are the hypothesis test and the confidence interval giving the same result? Explain

ON YOUR PAPER,  please confirm that you have read, understood and followed the exam instructions thoroughly.

Provide an appropriate response.In a survey, 26 voters were asked their ages. The results are shown below. 43  56  28  63  67  66  52   48  37   51   40    60   62 66  45  21  35  49  32  53   61   53   69   31   48   59a) Construct a frequency distribution to represent the data (with 5 classes beginning with a lower class limit of 20 and a class width of 10). Also state all the class midpoints and class boundaries (9pts) b) Construct a frequency histogram for the data. Determine the distribution shape of the data. Make sure to label all the axes (7pts) c) Construct a cumulative frequency distribution for the data. Then construct an ogive graph for the data. Make sure to label all the axes (10pts) d) Construct a frequency polygon for the data. Make sure to label all the axes (5pts) g) Construct a stem and leaf plot for the data (5pts) h) List the 5-number summary. Make sure to include the calculator command (4pts) i) Construct a box-plot for the data (5pts)

Find the indicated probability. (4pts)A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 5 first serves in? Assume that each serve is independent of the others. Make sure to first define variable X, then calculate the probability Define variabale X=

The graduate practical nurse understands that the influenza virus lives in the respiratory tract. In the chain of infection this is known as the