Question

Theodore is the owner of FlightPro (an app that provides maps and real-time weather reports for pilots) and is not satisfied with the current mean customer satisfaction rating for his app in the Google Play store. He reads the comments and sees that most of the complaints are based on the long download times for maps. So, he hires a software developer to reprogram the map feature in FlightPro with the hope that map download speeds will decrease and he will be able to achieve a customer satisfaction rating of at least 4.0 stars. Theodore examines the data for the sample of 36 customer ratings received in the two months following the software update and finds a mean of 4.2 with a standard deviation of 1.2. Which reason below does not explain why Theodore should use a t-score instead of a z-score to evaluate customer satisfaction ratings?

Please answer with a,b,c,d, and explain your response in great detail so I understand. Thank You :0) Thank You :0)

a. Theodore does not have a population mean.

b. Theodore is examining a sample of over 30 scores.

c. Theodore is comparing his sample to a mean goal.

d. Theodore does not have a population standard deviation.

Answer 1

# The formula for calculating the z-score is

where and are population mean and population standard deviation

from (a) and (d) it is given that population mean and population standard deviation is unknown,so that Theodore cannot go for z-score. In such cases ,we calculate t-score and When the sample size is small,we go for t-score. Because when the sample size is large, sufficient to assume the Cnetral Limit Theorem to hold, that means the distribution of the sample means follows normal distribution. we go for z-score when the assumption of normality satisfied. In this case since the sample size is small,we calculate t-score.

when standard deviation is unknown and smple size is small, we go for t-score instead of z-score.

# z-score ranges from -3 to 3 and t-score ranges from 20 and 80. There from (b) indicates that he is calculated t-scores. And it is easy to deal with t-scores because derived result can never be negative .Also ,since it covers a higher range it is more prefferable.

#from (c) , we use one sample t-test when we want to determine whether a sample mean is different from a known or hypothesized population mean.

the test statistic is

  

where ,

- sample mean

- hypothesized population mean

- sample standard deviation

- sample size.

If you need any further clarification ,please comment