Question

Sleep: Assume the general population gets an average of 7 hours of sleep per night. You randomly select 45 college students and survey them on their sleep habits. From this sample, the mean number of hours of sleep is found to be 6.89 hours with a standard deviation of 0.25 hours. You claim that college students get less sleep than the general population. That is, you claim the mean number of hours of sleep for all college students is less than 7 hours. Test this claim at the 0.01 significance level.

(a) What type of test is this?

-This is a two-tailed test.

-This is a left-tailed test.    

-This is a right-tailed test.

(b) What is the test statistic? Round your answer to 2 decimal places.
t- _{x =}

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis?

-reject H₀

-fail to reject H₀    

(e) Choose the appropriate concluding statement.

-The data supports the claim that college students get less sleep than the general population.

-There is not enough data to support the claim that college students get less sleep than the general population.     

-We reject the claim that college students get less sleep than the general population.

-We have proven that college students get less sleep than the general population.

Answer 1

Solution :

Given that,

Population mean = = 7

Sample mean = = 6.89

Sample standard deviation = s = 0.25

Sample size = n = 45

Level of significance = = 0.01

a)

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 7

Ha: 7

b)

The test statistics,

t = ( - )/ (s/)

= ( 6.89 - 7 ) / ( 0.25 / 45 )

= -2.41

c)

P- Value = 0.0025   

The p-value is p = 0.0025 < 0.01, it is concluded that the null hypothesis is rejected.

d)

Reject H0

Conclusion :

c)

The data supports the claim that college students get less sleep than the general population.