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4 June, 11:10

Watching TV: In 2012, the General Social Survey asked a sample of 1326 people how much time they spent watching TV each day. The mean number of hours was 3.02 with a standard deviation of 2.64. 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 differs from the claim? Use the = α0.05 level of significance and the P-value method with the TI-84 Plus calculator.

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  1. 4 June, 14:34
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    We fail to reject H₀ as there is insufficient evidence at 0.5% level of significance to conclude that the mean hours of TV watched per day differs from the claim.

    Step-by-step explanation:

    This is a two-tailed test.

    We first need to calculate the test statistic. The test statistic is calculated as follows:

    Z_calc = X - μ₀ / (s / √n)

    where

    X is the mean number of hours μ₀ is the mean that the sociologist claims is true s is the standard deviation n is the sample size

    Therefore,

    Z_calc = (3.02 - 3) / (2.64 / √ (1326))

    = 0.2759

    Now we have to calculate the z-value. The z-value is calculated as follows:

    z_α/2 = z_ (0.05/2) = z_0.025

    Using the p-value method:

    P = 1 - α/2

    = 1 - 0.025

    = 0.975

    Thus, using the positive z-table, you will find that the z-value is

    1.96.

    Therefore, we reject H₀ if | Z_calc | > z_ (α/2)

    Thus, since

    | Z_calc | < 1.96, we fail to reject H₀ as there is insufficient evidence at 0.5% level of significance to conclude that the mean hours of TV watched per day differs from the claim.
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