Question

You spoke with your instructor and she claimed that the average number of hours that you should study has to be more than 5 hours per week which will help you achieve an above average grade on any subject. She also suggested as a practice that you can test her claim and let her know what your conclusion is. So you decided to contact your peers and gather information to conduct a hypothesis to test your instructors claim.

Questions:

1. Contact at least 15 peers (they don’t have to be from the same class) and obtain how much time they study each week.

2. If you are to conduct a hypothesis test using the data you gathered,
   1. Which test (t test or z test) do you think be appropriate and why?
      (Hint: think about whether you have the population or sample standard deviation available)

2. Is this a test on population proportion or mean?

3. Calculate the sample statistics (sample mean or sample proportion based on the information given) (1 mark)

4. Use the data set you gathered to conduct a hypothesis test to determine your instructor’s claim. Use 0.05 level of significance. Please show your work, the 5 steps as described in the textbook.

3. Construct a 95% confidence interval for the population mean number of hours. Show your work.

Answer 1

a) In order to collect a sample that can give an unbiased and efficient estimate you should have a sample representing the complete population. In this way, you should have the minimum number of the sample which has been suggested as at least 15 as well as sample must be a representative of entire classes in the institute. You can divide your sample in the number of classes you have to sample into to ensure representation. If the number of classes is more than 5 then you should sample at least 5 in a class because less than 5 samples would not be able to give a good estimate of the variable of interest.

b)

1- In this particular case, the t-test would be an appropriate tool for hypothesis testing. This is because of two main reasons, firstly the sample is less than 30 so for the safer side it would be better to use the t-test. Secondly, the population standard deviation is not given so again t-test would give a better estimate for unknown standard deviation.

2- Of course, this is a test for the population mean because we are interested to test the average number of hours that one should study has to be more than 5 hours per week which will help you achieve an above-average grade on any subject.

3- To calculate sample statistics, gather the information ( number of hours they study) from selected samples and calculate the mean of all values. That sample mean would be sample statistics.

4- I don't know what were those steps as described in your textbook. I would try to explain the steps you can break them accordingly. At first, you should describe the hypothesis according to the problem you are solving.

then calculate the sample statistic(sample mean) from the gathered sample. In the next step, you should go for t-value, as given by

• t = t-statistic
• m = mean of the group
• µ = theoretical value or population mean
• s = standard deviation of the group
• n = group size or sample size

In the next step find your Critical value at n-1 degree of freedom in t-table at 0.05 level of significance.

In the final step state your conclusion whether to reject or accept the null hypothesis. That is if the t-value is greater than the critical value then reject the null hypothesis otherwise accept it.

c) The confidence interval is given by

where xbar is the calculated sample mean and t is a critical value obtained above.

Thanks