Question

Justine is an analyst for a sleep study center. She believes that the average adult in a certain city spends more than 7.2 hours sleeping daily. To test this claim, she selects a random sample of 63 adults from the city. The following is the data from this study:

• The alternative hypothesis Ha:μ>7.2.
• The sample mean number of hours slept per night by the 63 adults is 7.52 hours.
• The sample standard deviation is 1.14 hours.
• The test statistic is calculated as 2.23.

Using the information above and the portion of the t− table below, choose the correct p− value and interpretation for this hypothesis test.

Values for right-tail areas under the t-distribution curve

Probability	0.10	0.05	0.025	0.01	0.005
Degrees of Freedom
60	1.296	1.671	2.000	2.390	2.660
61	1.296	1.670	2.000	2.389	2.659
62	1.295	1.670	1.999	2.388	2.657
63	1.295	1.669	1.998	2.387	2.656
64	1.295	1.669	1.998	2.386	2.655
65	1.295	1.669	1.997	2.385	2.654
66	1.295	1.668	1.997	2.384	2.652
67	1.294	1.668	1.996	2.383	2.651
68	1.294	1.668	1.995	2.382	2.650
69	1.294	1.667	1.995	2.382	2.649

Select the correct answer below:

The probability of observing a value of t0=2.23 or more if the null hypothesis is true is between 0.05 and 0.10.

The probability of observing a value of t0=2.23 or more if the null hypothesis is true is between 0.01 and 0.025.

The probability of observing a value of t0=2.23 or less if the null hypothesis is true is between 0.01 and 0.025.

The probability of observing a value of t0=2.23 or more if the null hypothesis is true is between 0.025 and 0.05.

Answer 1

Given that, sample size = 63

sample mean = 7.52 and sample standard deviation = 1.14

The null and alternative hypotheses are,

H0 : μ = 7.2

Ha : μ > 7.2

Test statistic is,

=> Test statistic = t = 2.23

Degrees of freedom = 63 - 1 = 62

Using T-table we get, range of p-value at 62 degrees of freedom for test statistic = 2.23 is,

0.01 < p-value < 0.025

Answer : The probability of observing a value of t0=2.23 or more if the null hypothesis is true is between 0.01 and 0.025.