A scientist who studies teenage behavior was interested in determining if teenagers spend more time playing computer games then they did in the 1990s. In 1990s, the average amount of time spent playing computer games was 10.2 hours per week. Is the amount of time greater than that for this year? Fifteen students were surveyed and asked how many hours they spent playing video games. The test statistics is equal to 2.822. What is the p-value?

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12-11-2019
Mathematics

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A scientist who studies teenage behavior was interested in determining if teenagers spend more time playing computer games then they did in the 1990s. In 1990s, the average amount of time spent playing computer games was 10.2 hours per week. Is the amount of time greater than that for this year? Fifteen students were surveyed and asked how many hours they spent playing video games. The test statistics is equal to 2.822. What is the p-value?

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sitiadriani sitiadriani · Answer 1 · 2019-11-12T15:30:33+01:00

Answer:

- The amount of time greater than 10.2 hours for this year.

- The [tex]P_{value}[/tex] is 0.01358.

Step-by-step explanation:

Given information:

mean, X = 10.2 hours

sample, n = 15

using t distribution

test statistics = 2.822

[tex]P_{value}[/tex] = 2 x P([tex]t_{n-1}[/tex] > test statistics)

= 2 x P([tex]t_{15-1}[/tex] > 2.822)

= 2 x 0.00679

= 0.01358

[tex]P_{value}[/tex] is less than 0.10 which indicates that the amount of time greater than 10.2 hours for this year.

joaobezerra joaobezerra · Answer 2 · 2021-11-05T12:20:17+01:00

From the hypothesis test, it is found that the p-value is of 0.0068.

At the null hypothesis, we test if the mean is still the same, that is, of 10.2 hours per week, thus:

[tex]H_0: \mu = 10.2[/tex]

At the alternative hypothesis, we test if the mean has increased, that is, if it is greater than 10.2 hours per week, thus:

[tex]H_1: \mu > 10.2[/tex]

Fifteen students were surveyed, so there are 14 df. The test statistic is t = 2.822, and it is a one-tailed test, as we are testing if the mean is greater than a value.

Thus, using a t-distribution calculator, the p-value of the test is of 0.0068.

A similar problem is given at https://brainly.com/question/24166849