Suppose that ABC Software company is trying to develop “math software” for children in a rural area. The company wants to determine how much to charge. Based on the management experience and market trends, they think $60 is a reasonable price. The management team plans to charge $60 unless there is a substantial evidence that people are willing to pay more.

You are the statistician working for ABC. You are asked do some research and test the validity of their claim. You decided to conduct a survey to check how much people would be willing to pay for the software. You designed the survey and mailed to 50 potential customers; that is “n=50”. You receive 50 responses and you calculate the mean and the standard deviation;

= 65 and

= 10.

What does this result mean to you?

It will certainly be wrong to conclude that people will pay more for the software; why? Because if we asked different 50 people, we will have different results, the sample mean could change and it can be less than $60.

You remembered from Math 2 class that you should perform a hypothesis test to advise the management about the cost of the software.

You remembered to follow the steps:

Assume that the requirement for hypothesis testing methods mentioned in the textbook apply to your data.

Write down the null and alternative hypothesis.

c. Explain why you chose your hypotheses as such.

d. Do a hypothesis test of your data at the α = 5% level of significance for the population mean by carrying out the following six steps:

We will use “t-test” because the population standard deviation is not known. Write down the degrees of freedom, n-1.

View the example on how to use StatCrunch to compute the value tα

If it is left-tailed test, what is the critical value, -t0.05?

If it is right-tailed test, what is the critical value, t0.05?

If it is two-tailed test, what are the two critical values, ±t0.05?

Write down the test statistic, t0.

Write down the P-value.

Write down the sample size.

Write down the sample mean and sample standard deviation.

Use the “classical method” to reach your conclusion on whether or not to accept or reject the null hypothesis. Be sure to explain how you reached your conclusion.

Use the P-value to reach your conclusion on whether or not to accept or reject the null hypothesis. Be sure to explain how you reached your conclusion.

Explain with your own words what does it mean to accept or reject the null hypothesis in reference to this example.

Discuss you finding and advise the management.

Follow your primary posting with at least three substantive reply posts to your peers. In your response to classmates, you may discuss one of the following:

Ask your classmate a question about his/her result that is not clear to you.

Share something that you see about your classmate’s results that your classmate did not mention.

Share what you have learned from your classmate’s results.

Hypothesis Test for Population Mean using t-test

Hypothesis Testing – Population Mean – StatCrunch – Video