Question

Watching tv: in 2012, the general social survey asked a sample of 1310 people how much time they spend\t watching tv each day. The mean number of hours was 2.8 with a standard deviation of 2.6. A sociologist claims that people watch a mean of 3 hours of TV per day. Do the data provide sufficient evidence to conclude that the mean hours of TV watched per day is less the claim? Use the a=0.5 level of significance and the P-value method with the TI-84 Plus calculator.

(a) State the appropriate null and alternate hypotheses.

H0: Mu = 3
H1: Mu < 3

This hypothesis test is a _____ test.

(b) Compute the P-value. Round the answer to at least four decimal places

P-value =

Answer 1

a) Null hypothesis:
`\mu \geq 3`

Alternative hypothesis:
`\mu < 3`

This hypothesis test is a left tailed test.

b)
`t=(2.8-3)/((2.6)/(√(1310)))=-2.784`

The p value for this case can be calculated with this probability:

`p_v =P(z<-2.784)=0.0027`

We can conduct the test with the Ti84 using the following steps:

STAT>TESTS>T-test>Stats

We input the value
`\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310` and for the alternative we select
`< \mu_o`. Then press Calculate.

And we got the same results.

Explanation:

Information given

`\bar X=2.8` represent the sample mean

`s=2.6` represent the population standard deviation

`n=1310` sample size

`\mu_o =3` represent the value to test

`\alpha=0.5` represent the significance level for the hypothesis test.

t would represent the statistic

`p_v` represent the p value for the test

Part a) System of hypothesis

We want to test if the true mean is less than 3, the system of hypothesis would be:

Null hypothesis:
`\mu \geq 3`

Alternative hypothesis:
`\mu < 3`

This hypothesis test is a left tailed test.

Part b

The statistic is given by:

`t=(\bar X-\mu_o)/((s)/(√(n)))` (1)

Replacing the info given we got:

`t=(2.8-3)/((2.6)/(√(1310)))=-2.784`

The p value for this case can be calculated with this probability:

`p_v =P(z<-2.784)=0.0027`

We can conduct the test with the Ti84 using the following steps:

STAT>TESTS>T-test>Stats

We input the value
`\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310` and for the alternative we select
`< \mu_o`. Then press Calculate.

And we got the same results.