Question

Assume that you have a sample of n1=7?, with the sample mean X1=42?, and a sample standard deviation of S1=4,and you have an independent sample of n2=13 from another population with a sample mean of X2=33 and the sample standard deviation S2=6.

a. What is the value of the? pooled-variance tSTAT test statistic for testing H0: ?1=?2??

A local college newsletter reported that the average American college student spends one hour? (60 minutes) on a social media website daily. But you wonder if there is a difference between males and females. Attached below is a sample of 60 users of the website? (30 males and 30? females) and their recorded daily time spent on the website

b. Assuming that the variances in the population of times spent on the website per day are? equal, is there evidence of a difference in the mean time spent on the website per day between males and? females? (Use a 0.05 level of? significance.)

Let ?1 be the mean daily time spent on the website for male college students and ?2 be the mean daily time spent on the website for female college students. Determine the hypotheses.

Nine experts rated two brands of coffee in a? taste-testing experiment. A rating on a? 7-point scale (1equals=extremely ?unpleasing, 7equals=extremely ?pleasing) is given for each of four? characteristics: taste,? aroma, richness, and acidity. The accompanying data table contains the ratings accumulated over all four characteristics.

c. At the 0.01 level of? significance, is there evidence of a difference in the mean ratings between the two? brands? Let ?1 be the mean rating for brand A and ?2 be the mean rating for brand. Determine the null and alternative hypotheses for this test.

Letn1=100?, X1=60?, n2=100?, and X2=40

D.At the 0.01 level of? significance, is there evidence of a significant difference between the two population? proportions? Determine the alternate hypotheses.

Answer 1

From the information, Let /t be the mean of first population and fi, be the mean of second population The null and alternative hypotheses are, Test the hypothesis at α-0.05 level of significance The value of pooled variance is, +2-2 (7-1)42+(13-1)6 7+13-2 = 29.33 The test statistic is calculated as, 42-33 29.33| |+ 7 13 - 3.545 The value of test statistic is, t 3.545