1. In a 2013 study, it was found that children between the ages of 3 and 8 should get no more than 120 minutes of screen time for entertainment each day. A child psychologist is concerned that the mean is actually higher than 120 minutes. She recruits 40 families with children between the ages of 3 and 8 and calculates the amount of time these children spend in front of a screen daily. She finds a sample average of 128.525 minutes. Assume it is known that the population standard deviation is 20 minutes.

We will conduct a test to see if there enough evidence to claim that the average number of minutes of screen time children between the ages of 3 and 8 get each day greater than 120 minutes at the 1% level of significance ( = 0.01)?

What are the null and alternative hypotheses?

a. H0:=120

Ha:>120

b. H0:x=120

Ha:x>120

c. H0:=120

Ha:<120

d. H0:x=120 Ha:x<120

2. Is a Z-test appropriate to use in this scenario? And compute the test statistic, and the p value

3. Based in Question 3, state your conclusion

a. We reject the null hypothesis. There is sufficient evidence to conclude that the average minutes of screen time children between the ages of 3 and 8 get each day is greater than 120 minutes.

b. We fail to reject the null hypothesis. There is not sufficient evidence to conclude that the average minutes of screen time children between the ages of 3 and 8 get each day is greater than 120 minutes.

Use the following scenario for Questions 4-6.

In a laboratory, a standard weight that is known to weigh 1000 grams is repeatedly weighed 9 times on the same scale to test if the scale is calibrated correctly. The resulting measurements yielded a sample mean weight of 998 grams. Assume that the weightings by the scale are normally distributed and that the population standard deviation of the measurements is 4 grams.

4. Which of the following represents a 95% confidence interval for the mean weights reported by the scale?

a. 9981.645(49)=(995.81,1000.19)

b. 10001.645(49)=(997.81,1002.19)

c. 9981.96(49)=(995.39,1000.61)

d. 10001.96(49)=(997.39,1002.61)

e. 9982.576(49)=(994.57,1001.43)

f. 10002.576(49)=(996.57,1003.43)

5. Based on the confidence interval, does it appear as if the scale needs to be recalibrated? Why?

a. Yes: 95% confidence interval contains 1000

b. Yes: 95% confidence interval is entirely above 1000

c. Yes: 95% confidence interval is entirely below 1000

d. No: 95% confidence interval contains 1000

e. No: 95% confidence interval is entirely above 1000

f. No: 95% confidence interval is entirely below 1000

6. Suppose the true population mean reading provided by the scale is actually 1000. If this process of weighing a 1000 gram weight was repeated 60 times and a 95% confidence interval was calculated for each, how many of these confidence intervals would we expect to contain 1000?

a. 0

b. 3

c. 30

d. 57

e. 60