Question

We are interested in the average amount of time De Anza students spend studying statistics each week. A survey of 32 De Anza students yields a sample average time of 14.4 hours spent studying statistics per week with a sample standard deviation of 1.9 hours. Conduct a hypothesis test using a 5% level of significance, to determine if the average time spent studying statistics each week by De Anza students is less than 15 hours.

1. Ho: _______________ Ha: ___________________

2. In words, CLEARLY state what your random variable X-bar or P' represents.

3. State the distribution to use for the test. If t, include the degrees of freedom. If normal, include the mean and standard deviation.

4. p-value = ______________ (numerical value)

In 1 – 2 complete sentences, explain what the p-value means for this problem.

5. Use the previous information to sketch a picture of this situation. CLEARLY label and scale the horizontal axis and shade the region(s) corresponding to the p-value. “Scale” means have at least 2 numbers on the axis.

6. Indicate the correct decision (“reject the null hypothesis” or “do not reject the null hypothesis”), AND the reason for it.

7. Write an appropriate conclusion, using a COMPLETE SENTENCE.

8. Give a 95% Confidence Interval for the true mean or proportion.

Confidence Interval: ( ___________________ , ____________________ )

Include a sketch of the graph of the confidence interval. Label the point estimate and the lower and upper bounds of the Confidence Interval.

9. Interpret the confidence interval in a complete sentence.

10. One of the following is a Type I error, one of the following is a Type II error. Indicate which is a Type I error, and which is a Type II error.

A. the average amount of time De Anza students spend studying statistics each week is at most 15 hours, when, in fact, it is more than 15 hours.

B. the average amount of time De Anza students spend studying statistics each week less than 15 hours, when, in fact, it is at least 15 hours.

C. the average amount of time De Anza students spend studying statistics each week is at least 15 hours, when, in fact, it is less than 15 hours.

D. the average amount of time De Anza students spend studying statistics each week is more than 15 hours, when, in fact, it is at most 15 hours.

Answer 1

Given the sample size and sample mean sample standard deviation .

1)The hypotheses are

2) Here represents the sample mean.

3) We are using t-distribution since the population standard deviation is not known. Degrees of freedom is

4)The test statistic is

The p-value is

5) Since the , we reject the null hypothesis.

The conclusion is :

We are 95% confident that  the average time spent studying statistics each week by De Anza students is less than 15 hours.