Question

1. Ramilda wants to see if other students in her class listen to podcasts for a longer amount of time than students across the country. She collects data from twenty students in her class concerning the number of minutes per day they listen to podcasts. On average people in the United States listen to podcasts for 93 minutes per day. The data from her participants are summarized below:

Participant	Minutes
1	150
2	45
3	67
4	221
5	30
6	109
7	78
8	126
9	135
10	58
11	89
12	90
13	93
14	108
15	119
16	185
17	100
18	109
19	189
20	167

1. What are the null and alternative hypotheses using mathematical notation (1 point)?

2. Compute the appropriate test statistic for testing the hypothesis (5 points).

3. Using  = .05, what do you conclude about how Remilda’s class compares to other students across the country in the amount of time they spend listening to podcasts? Be sure to provide the critical value in your answer (1.5 points).

Answer 1

Given: = 93, s = 113.4, = 49.84 , n = 20, = 0.05

(a) The Hypothesis:

H0: = 93

Ha: > 93

This is a right tailed Test.

(b) The Test Statistic: Since the population standard deviation is unknown, we use the students t test.

The test statistic is given by the equation:

(c) The Critical Value:   The critical value (Right Tail) at = 0.05, for df = 19, tcritical = +1.691

The p Value:    The p value (Right Tail) for t = 2.42, for degrees of freedom (df) = n-1 = 19, is; p value = 0.0105

The Decision Rule:   If tobserved is > tcritical, then Reject H0

Also if P value is < , Then Reject H0.

The Conclusion:

Since tobserved (2.44) is > tcritical (1.691), We Reject H0. There is sufficient evidence at the 95% significance level to conclude that the mean time spent on listening to podcasts is greater than 93.

___________________________________________________

Calculation for the mean and standard deviation:

Mean = Sum of observation / Total Observations

Standard deviation = SQRT(Variance)

Variance = Sum Of Squares (SS) / n - 1, where SS = SUM(X - Mean)².

Participant	Minutes	Mean	(X - Mean)2
1	150	113.4	1339.56
2	45	113.4	4678.56
3	67	113.4	2152.96
4	221	113.4	11577.76
5	30	113.4	6955.56
6	109	113.4	19.36
7	78	113.4	1253.16
8	126	113.4	158.76
9	135	113.4	466.56
10	58	113.4	3069.16
11	89	113.4	595.36
12	90	113.4	547.56
13	93	113.4	416.16
14	108	113.4	29.16
15	119	113.4	31.36
16	185	113.4	5126.56
17	100	113.4	179.56
18	109	113.4	19.36
19	189	113.4	5715.36
20	167	113.4	2872.96
Total	2268	Total	47204.8
Mean	113.4	Variance	2484.46316
		SD	49.84