Answer to Question #261067 in Statistics and Probability for Elop

Question #261067

Blood glucose levels for obese patients have a mean of 100 with a standard deviation of 15. A researcher thinks that a diet high in protein will have a positive or negative effect on blood glucose levels. A sample of 30 obese patients who have tried a high in protein diet have a mean glucose level of 94. Test the hypothesis that a diet high in protein has an effect on blood glucose using a z-test with a level of significance =.04. Z-table


1
Expert's answer
2021-11-23T17:05:29-0500

The following null and alternative hypotheses need to be tested:

"H_0:\\mu=100"

"H_1:\\mu\\not=100"

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is "\\alpha = 0.04," and the critical value for a two-tailed test is "z_c = 2.0537."

The rejection region for this two-tailed test is"R = \\{z: |z| > 2.0537\\}."

The z-statistic is computed as follows:



"z=\\dfrac{\\bar{x}-\\mu}{\\sigma\/\\sqrt{n}}=\\dfrac{94-100}{15\/\\sqrt{30}}=-2.19089"

Since it is observed that "|z| = 2.19089 >2.0537= z_c," it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is "p=2P(Z<-2.19089)=0.02846," and since "p = 0.02846 < 0.04=\\alpha," it is concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that the population mean "\\mu" is different than "100," at the "\\alpha = 0.04" significance level.

Therefore, there is enough evidence to claim that a diet high in protein has an effect on blood glucose, at the "\\alpha = 0.04" significance level.


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