a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? O A. Ho H =2 H > 2 B. Ho H 2 H: H <2 OC. Họ 1

The mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believe this figure. They randomly survey 8 employees. The number of sick days they took for the past year are as follows: 10; 5; 13; 3; 11; 8; 6; 9. Let X = the number of sick days they took for the past year. Should the personnel team believe that the mean number is about 10? Conduct a hypothesis test at the 5% level.Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)   t  =    Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence…

A university wanted to see whether there was a significant difference in age between its day staff and evening staff. A random sample of 35 staff members is selected from each group. The data are given below.  Test the hypothesis that there is no difference in age between the two groups. Use a =0.05.  Day Staff 22 24 24 23 19 19 23 22 18 21 21 18 18 25 29 24 23 22 22 21 20 20 20 27 17 19 18 21 20 23 26 30 25 21 25 Evening Staff 18 23 25 23 21 21 23 24 27 31 24 20 20 23 19 25 24 27 23 20 20 21 25 24 23 28 20 19 23 24 20 27 21 29 30

3.  Can SAT scores predict college performance?  Let x be a variable that represents SAT score of a computer science major, and let y be a variable that represents a student’s GPA upon graduation.  A random sample of n =15 computer science majors provided their SAT scores and GPAs: x 1232 1070 1086 1287 1130 1048 1121 1095 1135 1208 1333 1160 1186 1243 1261 y 3.52 2.91 2.4 3.47 3.47 2.37 2.4 2.24 3.02 3.32 3.59 2.54 3.19 3.71 3.58   The scatter diagram for the SAT score and GPA is given below:   (a)  Find the sample correlation coefficient r.  Truncate to two decimal places.  What does the value tell you about the data? (b)  Find the equation of the least squares line .  Truncate to four decimal places.  What does the slope mean? (c)  Find the value of the coefficient of determination .  Truncate to two decimal places.  What does this number mean? (d)  What is the predicted GPA if a computer science major got a…