Question

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average?

The Type II error is not to reject that the mean number of hours of sleep LTCC students get per night is at most seven when, in fact, the mean number of hours
a. is less than 7 hours
b. is at least 7 hours
c. is at most 7 hours
d. is more than 7 hours

Answer 1

Explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ ≤ 7

For the alternative hypothesis,

µ > 7

This is a right tailed test.

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 22

Degrees of freedom, df = n - 1 = 22 - 1 = 21

t = (x - µ)/(s/√n)

Where

x = sample mean = 7.24

µ = population mean = 7

s = samples standard deviation = 1.93

t = (7.24 - 7)/(1.93/√22) = 0.58

We would determine the p value using the t test calculator. It becomes

p = 0.28

Since alpha, 0.05 < than the p value, 0.28, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average.

The Type II error is not to reject that the mean number of hours of sleep LTCC students get per night is at most seven when, in fact, the mean number of hours is

d. is more than 7 hours

Answer 2

Explanation:

solution is attached