Question

Consider the information and analysis. Identify and fix the errors addressed below.

Market researchers from a tech company are beta testing a new feature on one of their smartphones. A randomly selected sample of phone users are beta testing the new feature for 6 months. They are asked to rate the feature from 1 to 10 in several categories.

If the overall average rating is greater than 8.0 they will promote the feature into production. Otherwise, they will continue develop on the feature based on the feedback.

The average from the sample of 119 beta testers is 8.17. Researchers assume the population standard deviation is 0.9 and use a significance level of 0.05 to test the average.

The null and alternative are:

The test statistic and p-value are:

?? : ?̅ = 8 ?? : ?̅ > 8

Conclusion:

? ???? ????????? = 8.17 − 8 = 0.189 0.9

? − ????? = 0.0197

There is no evidence the average rating of the new feature is more than 8. We fail to reject the null hypothesis.

1. There is an error in the null and alternative hypothesis. What is the error? How do we fix it?

2. There is an error in the test statistic. What is the error? How do we fix it?

3. There are errors in the conclusion. What are the errors? How do we fix them?

Answer 1

Answer:  

= 8, n=119, = 8.17, = 0.9, = 0.05

a)

there is error in Null and Alternative hypothesis. instead of sample mean ( ?̅ )

we should use population mean ( ). because we are interested in finding population mean ( ).

it can be fixed as follows.

Null and Alternative hypothesis is

Ho: 8

Ha: > 8

b)

test statistics should be as follows

calculate test statistics

z = 2.06

test statistics = 2.06

c)

The given P-Value is correct. We can calculate is as follows

now calculate P-value for right tailed test

P-Value = 1 - P(z < 2.06)

find P(z < 2.06) using normal z table

we get

P(z < 2.06) = 0.9803

P-Value = 1 - P(z < 11.79)

P-Value = 1 - 0.9803

P-Value = 0.0197

d)

since (P-Value = 0.0197) < ( = 0.05)

Reject the null hypothesis.

Conclusion:

therefore there is enough significant evidence to support the claim that the average

rating of the new feature is more than 8.