Question

1. The National Retail Federation claims that the average consumer spent $162 on Valentine’s Day in 2019. You believe the average consumer actually spent more than $162.   You are able to survey a random sample of 89 consumers, and your sample reports spending an average of $165 on Valentine’s Day, with a sample standard deviation of $13. Use this information to conduct the appropriate hypothesis test by going through the steps we discussed in lecture. Assume the alpha level is .05 (or 5%). The test statistic would be what? Compute this test using the appropriate formula.

Answer 1

Solution:
Null hypothesis H0: Mean = 162
Alternative Hypothesis Ha: Mean > 162
Sample size = 89
Sample mean = 165
Sample standard deviation = 13
Here we don't know the population standard deviation so we will use t test
test stat = (sample mean - population mean)/ Sample standard deviation/ sqrt(sample size) = (165-162)/13/sqrt(89) = 2.18
Df = 89-1 = 88
From t table we found p-value so p-value is 0.016
Here alpha value is 0.05, as we can see that p-value is less than alpha value(0.016<0.05) so we can easily reject null hypothesis. and we have significant evidence to support that the average consumer actually spent more than 162.