Question

Assume the gen. population gets an average of 7 hours of sleep per night. You randomly select 55 college students and survey them on their sleep habits. From this sample, the mean number of hours of sleep is found to be 6.83 hours with a standard deviation of 0.55 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 0.10 significance level.

(a) What type of test is this?

This is a right-tailed test.

This is a left-tailed test.     

This is a two-tailed test.

(b) What is the test statistic?  
t_x =  

(c) What is the critical value of t? round to 3 decimal places.
t_α =  

(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

Here we have to test that

Null hypothesis :

Alternative hypothesis :

where

n = 55

Sample mean =

Sample standard deviation = s = 0.55

Here population standard deviation is not known so we use t interval.

a) This is left tailed (one tailed) test.

b) Test statistic :

t = -2.292 (Round to 3 decimal)

Test statistic = -2.292

c) Critical value of t :

alpha = level of significance = 0.10

degrees of freedom = n - 1 = 55 -1 = 54

t critical value from excel using function :

=T.INV(0.10,54)

= -1.297 (Round to 3 decimal)

Critical value = -1.297

d)

Here test statistic < critical value

So we reject null hypothesis H0.

e)

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