Over the years, th e mean customer satisfaction rating at a local restaurant has been 75. The restaurant was recently Es remodeled, and now the management claims the mean customer rating, µ, is not equal to 75. In a sample of 37 customers chosen at random, the mean customer rating is 76.6 . Assume that the population standard deviation of customer ratings is 15.6. Is there enough evidence to support the claim that the mean customer rating is different from 75? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H1. Ho: u = 75 OSO H: µ # 75 D=0 ? (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. x-H The value of the test statistic is given by ". The p-value is two times the area under the curve to the right of the value of the test statistic. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. o One-tailed 0.3- O Two-tailed Step 2: Enter the test statistic. 0.2 (Round to 3 decimal places.) 0.1 Step 3: Shade the area represented by the p- value. (c) Based on your answer to part (b), choose what can be concluded, at the 0.10 level of significance, about the claim made by the management. 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 support the claim that the mean customer rating is not equal to 75. 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 support the claim that the mean customer rating is not equal to 75. Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean customer rating is not equal to 75.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...