1.Ms. Lisa Monnin is the budget director for Nexus Media Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.Sales ($) 127 137 140 159 136 138 Audit ($) 122 103 127 136 149 120 142At the 0.01 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff?(a) State the decision rule. (Round your answer to 3 decimal places.)Reject H0 if t >(b) Compute the pooled estimate of the population variance. (Round your answer to 2 decimal places.)Pooled variance(c) Compute the test statistic. (Round your answer to 3 decimal places.)Value of the test statistic2Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne attire with those of Calvin Klein. Assume the population standard deviations are not the same. The following is the amount ($000) earned per month by a sample of Claiborne models:$5 $4.5 $3.4 $3.4 $6 $3.3 $4.5 $4.6 $3.5 $5.24.8 4.4 4.6 3.6 5The following is the amount ($000) earned by a sample of Klein models.$3.1 $3.7 $3.6 $4 $3.8 $3.8 $5.9 $4.9 $3.6 $3.62.3 4(1) Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.)Degrees of freedom(2) State the decision rule for 0.05 significance level: H0: ?LC ? ?CK; H1: ?LC > ?CK. (Round your answer to 3 decimal places.)Reject H0 if t>(3) Compute the value of the test statistic. (Round your answer to 3 decimal places.)Value of the test statistic3A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. The information is summarized below.Statistic Men WomenSample mean 25.24 21.73 Population standard deviation 5.53 4.54 Sample size 34 37 ________________________________________At the .01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?(a) Compute the value of the test statistic. (Round your answer to 3 decimal places.)Value of the test statistic(b) What is your decision regarding on null hypothesis?The decision is the null hypothesis that the means are the same.(c) What is the p-value? (Round your answer to 4 decimal places.)p-valueSuppose the manufacturer of Advil, a common headache remedy, recently developed a new formulation of the drug that is claimed to be more effective. To evaluate the new drug, a sample of 270 current users is asked to try it. After a one-month trial, 251 indicated the new drug was more effective in relieving a headache. At the same time a sample of 390 current Advil users is given the current drug but told it is the new formulation. From this group, 352 said it was an improvement.(1) State the decision rule for .01 significance level: H0: ?n ? ?c; H1: ?n > ?c. (Round your answer to 2 decimal places.)Reject H0 if z >?(2) Compute the value of the test statistic. (Do not round the intermediate value. Round your answer to 2 decimal places.)Value of the test statistic5Lester Hollar is vice president for human resources for a large manufacturing company. In recent years he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the last six months. Below are the results.Employee Before After1 6 3 2 6 2 3 7 1 4 7 2 5 4 2 6 6 6 7 6 3 8 6 7 ________________________________________At the 0.10 significance level, can he conclude that the number of absences has declined? Hint: For the calculations, assume the “Before” data as the first sample.Reject H0 if t > . (Round your answer to 3 decimal places.)The test statistic is . (Round your answer to 3 decimal places.)?7 What is the critical F value for a sample of four observations in the numerator and seven in the denominator? Use a one-tailed test and the .01 significance level. (Round your answer to 2 decimal places