A household appliance company is interested in understanding the average price that consumers pay for a washing machine (for laundry). They obtained a random sample of 100 households to address this issue. In the sample, the average consumer reported paying $968. Assume you do not know the population mean, but you know that the population standard deviation is equal to $125. Using a significance level of 0.05, answer the questions below:

(a) Is there enough evidence to suggest that the average price differs from $1000? Conduct a hypothesis using the test statistic method and interpret your result. (6 points)

(b) Re-do part (a) using a significance level of 10%. (5 points)

(c) Re-do part (a) using the p-value method. (5 points)