Question

"A small electronics store has begun to advertise in the local newspaper.They claim that their sales are now greater than last year's, $9820. A random sample of 10 weeks while the ads were running had a sample mean of $10960 and the population standard deviation was $1580. Test the claim at the .05 level of significance.

Answer 1

This question is about hypothesis testing to determine if a store's sales are greater than last year's. The null hypothesis is that the population mean is equal to the claimed value, and the alternative hypothesis is that the population mean is greater than the claimed value. We calculate the test statistic and compare it to the critical value.

Step-by-step explanation:

This question is about hypothesis testing. The null hypothesis is that the population mean is equal to the claimed value, and the alternative hypothesis is that the population mean is greater than the claimed value. The test statistic is calculated as (sample mean - claimed value) / (population standard deviation / sqrt(sample size)).

In this case, the test statistic is (10960 - 9820) / (1580 / sqrt(10)) = 404.78. Using the t-distribution with 9 degrees of freedom (10-1), we find the critical value for a one-tailed test with a significance level of 0.05 to be 1.833. Since the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is evidence to support the claim that the store's sales are greater than last year's.