Over the years a sushi restaurant has had a mean customer
Last updated: 5/13/2023
Over the years a sushi restaurant has had a mean customer satisfaction rating of 72 5 with a variance of 25 4 The owner wants to see if using a new menu will have any effect on the variance o The owner surveys a random sample of 14 customers who ordered from the new menu For the customers surveyed the variance of ratings is 46 2 Assume the ratings for customers who order from the new menu follow a normal distribution Is there enough evidence to conclude that the population variance differs from 25 4 To answer complete the parts below to perform a hypothesis test Use the 0 10 level of significance a State the null hypothesis H and the alternative hypothesis H that you would use for the test Ho H 0 0 S O O Chi square Distribution Step 1 Enter the number of degrees of freedom Step 3 Enter the test statistic Round to 3 decimal places Step 2 Select one tailed or two tailed O One tailed O Two tailed b Perform a chi square test and find the p value Here is some information to help you with your chi square test Step 5 Enter the p value Round to 3 decimal places X The value of the test statistic is given by x n 1 s G Step 4 Shade the area represented by the p value Osa The p value is two times the area under the curve to the right of the value of the test statistic 0 0 Since the O O 5 D 3 12 424 0 1 Yo Since the p value is less than or equal to the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the variance differs from 25 4 c Based on your answer to part b choose what can be concluded at the 0 10 level of significance about the population variance of ratings for customers who order from the new menu Since the p value is less than or equal to the level of significance the null hypothesis is not rejected So there is not enough evidence to conclude that the variance differs from 25 4 Since the p value is greater than the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the variance differs from 25 4 is ir greater than the lovel of X X S TERE A M