Question

For Apple’s newly developed television, the emitted radiation level is normally distributed N(μ, σ2) with unknown μ and σ2. The FCC requires that the mean emitted radiation level be below 0.50 mr/hr (milliroentgens per hour). A random data sample of radiation levels from 16 of the new Apple televisions gives a sample mean of 0.51 mr/hr and gives a sample standard deviation of 0.20 mr/hr.

Formulate the hypothesis test that an FCC inspector would use to check if there is sufficient evidence to conclude that Apple televisions satisfy the FCC requirement on the mean emitted radiation level.

Calculate the appropriate test statistic for hypothesis test in (a). Use the notation ztest, ttest, X2test, or ftest.

Conclude whether Apple televisions satisfy the FCC requirement on the mean emitted radiation level at the 0.01 level of significance.

Calculate the P-value for the test.

Answer 1

The Hypothesis:

H0: = 0.5

Ha: < 0.5

This is a Left Tailed Test.

The Test Statistic: Since population standard deviation is unknown, and n < 30, we use the students t test.

The test statistic is given by the equation:

The p Value: The p value (Left Tail) for t =0.2, for degrees of freedom (df) = n-1 = 15, is; p value = 0.4221

The Decision Rule:   If P value is < , Then Reject H0.

The Decision:   Since P value (0.4221) is > (0.01) , We Fail to Reject H0.

The Conclusion: There is isn’t sufficient evidence at the 99% significance level to conclude that the Apple Televisions are satisfying the FF requirement of the mean radiation levels being less than 0.5 mr/hr.