A simple random sample of 28 Lego sets is obtained and the number of pieces in each set was counted. The sample has a standard deviation of 12.65. Use a 0.05 significance level to test the claim that the number of pieces in a set has a standard deviation different from 11.53.

Step-by-step explanation:

Given that:

A simple random sample n = 28

sample standard deviation S = 12.65

standard deviation = 11.53

Level of significance ∝ = 0.05

The objective is to test the claim that the number of pieces in a set has a standard deviation different from 11.53.

The null hypothesis and the alternative hypothesis can be computed as follows:

Null hypothesis:

Alternative hypothesis:

The test statistics can be determined by using the following formula in order to test if the claim is statistically significant or not.

From the chi-square probabilities table at 0.975 and degree of freedom 27;

= 14.573

From the chi-square probabilities table at 0.975 and degree of freedom 27;

43.195

Decision Rule: To reject the null hypothesis if ; otherwise , do not reject the null hypothesis:

The rejection region is

Conclusion:

We fail to reject the null hypothesis since  test statistic value 32.5002125  lies  between 14.573 and 43.195.

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step-by-step explanation: