1. Suppose a sample of university students were asked the question, "In hours, what was your phone screen time yesterday?"

Some researchers wish to know if the average daily phone screen time of university students is significantly different from 4 hours. That is, they wish to test the hypotheses

H0:=4versusH1:4,

where denotes the mean average daily phone screen time of university students in hours.

Using the data collected, a one-sample t-test was carried out with the following results:

 One Sample t-test data: screentime t = -1.2674, df = 36, p-value = 0.2132 alternative hypothesis: true mean is not equal to 4 95 percent confidence interval: 3.547495 4.104456 sample estimates: mean of x 3.825976 

Answer the following questions, rounding your answers to three decimal places where relevant.

1. What is the test statistic? Answer
2. What is the degrees of freedom? Answer
3. What must the sample size be? Answer
4. What is the p-value? Answer
5. What is the sample mean? Answer
6. What is the LOWER bound of the confidence interval (i.e., the lower number in the confidence interval range)? Answer
7. What is the UPPER bound of the confidence interval (i.e., the higher number in the confidence interval range)? Answer

2. Now suppose a different sample of university students were asked the question, "In hours, what was your phone screen time yesterday?"

Some researchers wish to know if the average daily phone screen time of university students is significantly different from 4 hours. That is, they wish to test the hypotheses

H0:=4versusH1:4,

where denotes the mean average daily phone screen time of university students in hours.

Using the data collected, a one-sample t-test was carried out with the following results:

 One Sample t-test data: screentime t = -1.7955, df = 87, p-value = 0.07604 alternative hypothesis: true mean is not equal to 4 95 percent confidence interval: 3.593036 4.020661 sample estimates: mean of x 3.806848 

Which of the following statement(s) is/are true? (Assume a significance level of =0.05. Also assume that any reported p-values have been rounded to three decimal places).

Select one or more:

a.

The p-value suggests that, on average, at least 7.6% of students have a daily phone screen time of less than 4 hours

b.

Since we have a p-value that is less than the significance level, we can reject the null hypothesis

c.

Since we have a p-value that is greater than the significance level, we cannot reject the null hypothesis

d.

Since we have a p-value that is greater than the significance level, we can reject the null hypothesis

e.

If it is true that the average daily phone screen time of university students is equal to 4 hours, then the probability we would have seen a test statistic at least this extreme is 0.05

f.

Since we have a p-value that is less than the significance level, we cannot reject the null hypothesis

g.

If it is true that the average daily phone screen time of university students is equal to 4 hours, then the probability we would have seen a test statistic at least this extreme is 0.076

3. Now suppose a new sample of university students were asked the question, "In hours, what was your phone screen time yesterday?"

Some researchers wish to know if the average daily phone screen time of university students is significantly different from 4 hours. That is, they wish to test the hypotheses

H0:=4versusH1:4,

where denotes the mean average daily phone screen time of university students in hours.

Using the data collected, a one-sample t-test was carried out and the results were stored. Below are some facts about this test that will be useful for answering this question:

• n = 98
• df = 97
• x = 3.955
• t97,0.975 = 1.985
• s = 1.37

Using the above facts, your task is to calculate a 95% confidence interval. One of the options below is the correct 95% confidence interval. Choose the best answer, noting that there may be some minor differences between your answer and the best option below due to rounding:

Select one:

a.

(2.585,5.325)

b.

(2.955,4.955)

c.

(3.817,4.093)

d.

(3.681,4.229)