I need help with these 6 questions please

1.

Suppose an education administrator wants to know whether the test scores of a new standardized graduation exam are different for males and females. To test this hypothesis, the administrator decides to perform a t-test for two independent means. She takes a random sample of test scores from both male and female populations. Some of the summary data are shown in the table. . Population Sample Sample Sample standard Population , , _ . . Descnptlon Slze mean (pts) dewatnon (pts) Female .71] = 23 E1 = 34.9 31 = 3.14 2 Male :12 = 24 i2 = 35.3 52 = 3.88 The administrator assumes that the population variances are equal, so she computes a pooled ttest statistic. Determine the number of degrees of freedom, (If, for the pooled t-statistic. Two independent samples from normal distributions are being compared. The sample data are summarized in the table. , Population Sample Sample Sample standard Standard error Population . . . . mean Size mean devratlon estimate #1 (unknown) m = 16 31 = 15.3 31 = 2.010 SE = 0.503 2 [42 (unknown) n2 = 14 i2 = 13.8 52 = 2.330 SE2 = 0.623 The estimated standard error of the difference of the two sample means is SE = 0.800. Compute the value of the two-sample t-statistic used to test the null hypothesis H 01 M1 = 112- Please give your answer precise to three decimal places. Women stereotypically talk more than men do and researchers wondered how much more. Suppose a study attempted to determine the difference in the mean number of words spoken by men or women per day. The results of the study are summarized in the table. Population Sample Sample Sample standard Standard error Group mean size mean deviation estimate women Mw (unknown) nw = 47 Xw = 16177 Sw = 7520 SEw = 1097 men Mm (unknown) nm = 49 Xm = 16569 Sm = 9108 SEm = 1301 df = 91.9887 Assume the conditions are satisfied for a two-sample t-confidence interval. First, determine the positive critical value, t, for a 95% confidence interval to estimate how many more words women speak each day on average compared to men, "w - Mm. Give your answer precise to at least three decimal places. 1 = Determine lower and upper limits of a 95% confidence interval for how many more words speak each day on average compared to men. A negative number would indicate how many fewer words women speak each day on average compared to men. Give your answers precise to the nearest integer number of words. lower limit : upper limit :Suppose a grocery store is considering the purchase of a new self-checkout machine that will get customers through the checkout line faster than their current machine. Before he spends the money on the equipment, he wants to know how much faster the customers will check out compared to the current machine. The store manager recorded the checkout times, in seconds, for a randomly selected sample of checkouts from each machine. The summary statistics are provided in the table. Sample Sample Sample standard Group Description Standard error size mean (min) deviation (min) estimate (min) old machine n1 = 47 x1 = 124.4 S1 = 26.8 SE = 3.90918 2 new machine n2 = 44 X2 = 109.0 $2 = 21.2 SE2 = 3.19602 df = 86.63765 Compute the lower and upper limits of a 95% confidence interval to estimate the difference of the mean checkout times for all customers. Estimate the difference for the old machine minus the new machine, so that a positive result reflects faster checkout times with the new machine. Use the Satterthwaite approximate degrees of freedom, 86.63765. Give your answers precise to at least three decimal places. upper limit: lower limit:Determine the meaning of the lower and upper limits of the condence interval. 0 The probability is 95% that the difference in the mean checkout time of all customters using the new machine compared to the old one is within the bounds of the condence interval. 0 The store manager is 95% condent that the mean difference in checkout times for all customers using the new machine compared to the current one is contained in the calculated interval. 0 The probability is 95% that the mean difference in checkout times for all customers using the new machine compared to the current one is contained in the calculated interval. 0 The store manager is 95% condent that the dilference in the mean checkout time of all customers using the new machine compared to the current one is contained in the calculated interval. Suppose Laura, a facilities manager at a health and wellness company, wants to estimate the difference in the average amount of time that men and women spend at the company's fitness centers each week. Laura randomly selects 14 adult male fitness center members from the membership database and then selects 14 adult female members from the database. Laura gathers data from the past month containing logged time at the fitness center for these members. She plans to use the data to estimate the difference in the time men and women spend per week at the fitness center. The sample statistics are summarized in the table. Population Population mean Sample Population Sample mean Sample standard description (unknown) size (min) deviation (min) male n1 = 14 X1 = 120.1 $1 = 40.3 N female n2 = 14 X2 = 104.5 $2 = 25.9 df = 22.174 The population standard deviations are unknown and unlikely to be equal, based on the sample data. Laura plans to use the two- sample t-procedures to estimate the difference of the two population means, M1 - M2. First, compute the estimated standard error, SE, of the difference in the sample means that Laura uses to construct the confidence interval. Provide your answer precise to at least three decimal places. SE = min Next, compute the margin of error, m, for the 95% confidence interval for the difference of the population means using software or a table of t-distributions. If you are using software, you may find some software manuals helpful. Provide your answer precise to at least one decimal place.\fSuppose a researcher wishes to construct a 99% t-confidence interval for the difference of two independent means with unknown population standard deviations. His sample sizes are n = 7 and n2 = 10, and his calculated Satterthwaite approximate degrees of freedom are 12.513. What is the positive t-critical value for this confidence interval, rounded to 3 decimal places? t =