Question

Researchers wanted to test whether viewing a scary movie before going to bed affects the number of hours people sleep. 40 students were asked to participate. Each of these students was asked to watch a scary movie within an hour of going to bed, and the number of hours they slept was recorded. The mean number of hours slept for these students was 5.5 hours. In general, students sleep an average of 7 hours per night with a standard deviation of 1 hour. Use the hypothesis testing procedure to determine if there is a difference between individuals who watch a scary movie before bed and those who do not on number of hours slept (α = .05)

Answer 1

Solution:

The null and alternative hypotheses are as follows:

i.e. The mean of the number of hours slept by individuals who watch scary movie before bed is equal to the general individual's average of 7 hours.

  i.e. The mean of the number of hours slept by individuals who watch scary movie before bed is not equal to the general individual's average of 7 hours.

To test the hypothesis we shall use z-test for single mean. The test statistic is given as follows:

Where, x̄ is sample mean, μ is the value of population mean specified under H_{​​​​​​0}, σ is population standard deviation and n is sample size.

We have, x̄ = 5.5 hours, μ = 7 hours, σ = 1 hour and n = 40

The value of the test statistic is -9.4868.

Since, our test is two-tailed test, therefore we shall obtain two-tailed p-value for the test statistic. The two-tailed p-value is given as follows:

p-value = 2P(Z < value of the test statistic)

p-value = 2P(Z < -9.4868)

p-value = 0.00000

Significance level (α) = 0.05

(0.00000 < 0.05)

Since, p-value is less the significance level of 0.05, therefore we shall reject the null hypothesis (H_{​​​​​​0}) at 0.05 significance level.

Conclusion: At α = .05, there is enough evidence to conclude that there is a difference between individuals who watch a scary movie before bed and those who do not on number of hours slept.

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