Marcy's Consignment shop is based in Port Angeles, Washington. It offers both male and female never or slightly used clothing and accessories on a consignment basis.
Marcy's recently redesigned their website and wants to show that sales have increased.
The sales manager selects 30 sales records at random from the store's online client list
And she finds a mean increase in spending of $3.50 with a standard deviation of $7.20.
The resulting P-value for anα of 0.05 is
A) 0.012
B) 0.315
C) 0.630
D) 0.006
E) 0.024

Question

Quizplus · Accepted Answer

To find the P-value, we need to conduct a one-sample t-test with the following hypotheses:
Null hypothesis: The mean increase in spending is $0.
Alternative hypothesis: The mean increase in spending is greater than $0 (since we want to show that sales have increased).

Using the given information, we can calculate a t-statistic:

t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
t = (3.50 - 0) / (7.20 / sqrt(30))
t = 2.63

Using a t-table with 29 degrees of freedom (since we have 30 minus 1 degrees of freedom), and an α of 0.05, we can find the critical t-value to be 1.699.

Since our calculated t-value (2.63) is greater than the critical t-value (1.699), we have evidence to reject the null hypothesis in favor of the alternative hypothesis.

The P-value is the probability of obtaining a t-value as extreme or more extreme than our calculated t-value, assuming the null hypothesis is true. Since our alternative hypothesis is one-tailed (since we are only interested in increases in spending), we need to find the area to the right of our calculated t-value in the t-distribution.

Using a t-table or calculator, we find a P-value of 0.006.

Since this P-value is less than our α of 0.05, we have evidence to reject the null hypothesis and conclude that there is a significant increase in spending at Marcy's Consignment shop. Therefore, the best choice is D.

Marcy's Consignment Shop Is Based in Port Angeles, Washington