Question

10. The owner of a company has asked you to conduct an evaluation of the customer satisfaction ratings to see if the company continues to provide customers with customer service that ranks above average. To be considered above average the average customer satisfaction score has to be above 7. Suppose a random sample of 60 customers is taken from a population to evaluate customer satisfaction. The sample mean is 7.25. The sample standard deviation is 1.05. The population mean is hypothesized to be 7. The level of significance is .025. A rating greater than 7 allows the company to advertise on its website and in its marketing campaign that the company consistently provides an above average customer experience. a. What is the null hypothesis and alternative hypothesis? b. Is this a one tail or two tail test? Explain. Recall the 3 general forms for specifying the Null and Alternative hypotheses (One tail right, One tail left, and two tail). c. Draw a diagram to represent the sampling distribution of x-bar based on the hypothesized mean value stated in the null hypothesis. Explain the important features of this distribution. Where is this distribution centered? What is the spread of the distribution? Label the axis. d. Draw a second diagram and shade the area of getting a sample mean that is greater than or equal to 7.25. e. What is the value of the test statistic? This calculation involves converting the x-bar value to either a z or a t. Is the test statistic a z or a t? Show an equation and calculation to support the value of the test statistic you entered above. f. In hypothesis testing a critical value is used to help us determine if the null hypothesis is "rejected" or if the decision is to "do not reject" the null hypothesis. What is the critical value in this example? Is this a z or a t? g. Draw a diagram and shade the area that represents the probability of getting a t value that is greater than or equal to the test statistic. Label the axis. Label the value of the test statistic on the diagram. Label the shaded area with a probability (since this uses the t table you can only approximate this value). h. What is the p-value (numerical value)? i. What is the value for the confidence coefficient in this example? j. If you add the value of the confidence coefficient and a the sum will equal k. What is the level of significance in this question? 1. Based on your calculations do "reject" or "do not reject" the null hypothesis? Explain how you decided. m. Interpret you result. Write a short answer explaining what your decision means (What is your conclusion about the level of customer satisfaction for your company).

Answer 1

ca) Hoil = 7 Hall 77 Tonetailed Right. since we are interested only on one direction hot for both. 7 7.25 7 7.25 -(e) test statistic. = X-M. -1.257 1.os t = 1.84437 18443 testshahistic is

(f critical value = t 590.025 = 2.00 lol this ist 18442 2.oolo 13493 (6) pralue=P(T897 1.8443) To.0351 ( gsolo 2 = 0.025 toys so.gts 12 -0.025 do not reject. since Pralue xa There is notruthciente-i dence to unelude that that, average customer a satisfaction a score has to be a bove?