Question

Sleep (Raw Data, Software Required):
Assume the general population gets an average of 7 hours of sleep per night. You randomly select 35 college students and survey them on the number of hours of sleep they get per night. The data is found in the table below. 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 left-tailed test. This is a right-tailed test.     This is a two-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.

DATA ( n = 35 ) Sleep per Night College Students Hours    5.0 6.6 7.3 6.4 7.3 4.6 7.8 5.7 8.7 4.8 3.6 4.8 5.3 9.3 9.9 6.5 8.8 5.1 4.7 7.0 5.0 7.4 4.4 7.5 5.7 5.8 7.3 6.4 6.1 7.6 7.1 9.7 7.3 7.1 5.2

Answer 1

Solution:

= 7

Claim: college students get less sleep than the general population.

i.e. <  7

So hypothesis are

H0: = 7    ....null hypothesis

H1: <  7 ....alternative hypothesis

Given , We are given a sample of size n = 35

n = 35 ....sample size

Use excel or calculator to find the sample mean and sample SD s of the given data.

Excel function for : =average(data)

Excel function for s   : =stdev(data)

= 6.537143

s = 1.580783

= 0.10 .... level of significance

a) This is a left-tailed test.  

(Because there is < sign in H1

b) The test statistic t is

t =  

= (6.537143 - 7)/(1.580783/35)

= -1.73

c) Degrees of freedom = n -1 = 35 - 1 = 34

t = -1.73

Left tailed test i.e.one tailed left sided

Using this information

p value = 0.0464

d) Since p value is less than = 0.10

reject H₀    

e)concluding statement.

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