A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. It was desired to test to determine if the mean age of all female purchasers exceeds the mean age of all male purchasers. The sample data is shown here: Female: n = 20, sample mean = 50.30, sample standard deviation = 13.215 Male: n = 20, sample mean = 39.80, sample standard deviation = 10.040 Use the pooled estimate of the population standard deviation to calculate the value of the test statistic to use in this test of hypothesis.
A) t = 2.17
B) t = 2.65
C) t = 2.83
D) t = 3.17

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula for the t-test for independent samples with equal variances: t = (mean1 - mean2) / (sp * sqrt(2/n)), where sp is the pooled standard deviation. The pooled standard deviation sp is calculated as sqrt(((n1-1)*s1^2 + (n2-1)*s2^2) / (n1+n2-2)). Substituting the given values, the test statistic t is approximately 2.83.

A Marketing Study Was Conducted to Compare the Mean Age