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Sagot :
Using the t-distribution, it is found that the most appropriate conclusion for the hypotesis test is given by:
Phone use did not change.
What are the hypothesis tested?
At the null hypothesis, we test if the mean has not changed, that is:
[tex]H_0: \mu = 0[/tex]
At the alternative hypothesis, we test if it has changed, that is:
[tex]H_1: \mu \neq 0[/tex].
What is the test statistic?
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
- [tex]\overline{x}[/tex] is the sample mean.
- [tex]\mu[/tex] is the value tested at the null hypothesis.
- s is the standard deviation of the sample.
- n is the sample size.
In this problem, the values of those parameters are as follows:
[tex]\overline{x} = -0.2, \mu = 0, s = 9.1, s = 200[/tex]
Hence, the test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{-0.2 - 0}{\frac{9.1}{\sqrt{200}}}[/tex]
t = 0.31.
What is the conclusion?
Considering a two-tailed test, as we are testing if the mean is different of a value, with a standard significance level of 0.05 and 200 - 1 = 199 df, the critical value is of [tex]|t^{\ast}| = 1.972[/tex].
Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis and the conclusion is:
Phone use did not change.
More can be learned about the t-distribution at https://brainly.com/question/26454209
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