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34kurt
2 years ago
11

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic t.

Mathematics
1 answer:
lawyer [7]2 years ago
8 0

Using the t-distribution, it is found that the p-value of the test is 0.007.

At the null hypothesis, it is <u>tested if the mean lifetime is not greater than 220,000 miles</u>, that is:

H_0: \mu \leq 220000

At the alternative hypothesis, it is <u>tested if the mean lifetime is greater than 220,000 miles</u>, that is:

H_1: \mu > 220000.

We have the <u>standard deviation for the sample</u>, thus, the t-distribution is used. The test statistic is given by:

t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}

The parameters are:

  • \overline{x} is the sample mean.
  • \mu is the value tested at the null hypothesis.
  • s is the standard deviation of the sample.
  • n is the sample size.

For this problem:

\overline{x} = 226450, \mu = 220000, s = 11500, n = 23

Then, the value of the test statistic is:

t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}

t = \frac{226450 - 220000}{\frac{11500}{\sqrt{23}}}

t = 2.69

We have a right-tailed test(test if the mean is greater than a value), with <u>t = 2.69</u> and 23 - 1 = <u>22 df.</u>

Using a t-distribution calculator, the p-value of the test is of 0.007.

A similar problem is given at brainly.com/question/13873630

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