Question

Explain how to solve using RStudio:

A national computer retailer believes that the average sales are greater for salespersons with a college degree. A random sample of 31 salespersons with a degree (group 1) had an average weekly sale of $3411 last year, while 32 salespersons without a college degree (group 2) averaged $3112 in weekly sales. The standard deviations were $468 and $642 respectively. Is there evidence at the 5% level to support the retailer's belief?

a. Select the Alternate hypothesis

b. Select the p-value for this hypothesis test.

c. Select the Decision to Reject H₀ or Failure to Reject H₀

I know that the alternate hypothesis is μ1 > μ2, but i need help finding the step b and step c using RStudio.

Answer 1

Given that,

For group 1 : $n_1 = 31, \bar x_1 = \$3411, \sigma_1 = \$468$

For group 2 :

$31 12.T2 = $642 n-= 32.2.2

a) The null and alternative hypotheses are,

$H_0: \mu_1 = \mu_2$

Ha : μ1 > μ2

Test statistic is,

3411 - 3112 T1-T2 (468)2(642)2 31 12 7t

b) p-value= P(Z >2.12) =1 - P(Z <2.12)= 1 - 0.9830 = 0.0170

=> p-value = 0.0170

c) Since, p-value = 0.0170 < 0.05

we reject the null hypothesis OR reject H₀.