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Test the hypothesis that the average yield strength of a particular type of steel is 100...

Test the hypothesis that the average yield strength of a particular type of steel is 100 ksi if the performance of a random sample of 8 specimens resulted in the following: 102, 97, 101, 98, 99, 96, 103, and 98 ksi. Use a 0.05 level of significance and assume that the distribution of strength is normal.

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Answer #1

Null Hypothesis

Alternative Hypothesis

Since population standard deviation is unknown, we use t -distribution here.

Under H0, the test statistic is

The sample mean is

The Sample standard deviation is

The test statistic is

Degrees of freedom = n-1= 7

The critical value of t for 7 df at 5% significance level is +/-2.365

The P-Value is 0.4229

Since p value is gretare than significance level. Fail to REject H0.

Hence, the average yield strength of a particular type of steel is 100 ksi.

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