Math / Data & Statistics

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A random sample of size 13 from a normal distribution has standard deviation $s=51$ . Test $H_{0}: \sigma=46$ versus $H_{1}: \sigma>46$ . Use the $\alpha=0.01$ level of significance. Part: $0 / 5$
Part 1 of 5
The hypotheses are provided above. This hypothesis test is a (Choose one) $\nabla$ test.

Studdy Solution

STEP 1

1. The sample is drawn from a normal distribution.
2. The sample size is $n = 13$ .
3. The sample standard deviation is $s = 51$ .
4. The null hypothesis is $H_0: \sigma = 46$ .
5. The alternative hypothesis is $H_1: \sigma > 46$ .
6. The level of significance is $\alpha = 0.01$ .

STEP 2

1. Identify the type of test to use.
2. Determine the test statistic.
3. Find the critical value.
4. Compare the test statistic to the critical value.
5. Make a decision to reject or fail to reject the null hypothesis.

STEP 3

Identify the type of test to use.
Since we are testing a hypothesis about the population standard deviation and the sample is from a normal distribution, we use a chi-square ( $\chi^2$ ) test.
The hypothesis test is a chi-square ( $\chi^2$ ) test.

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