Question

A researcher studying stress is interested in the blood pressure measurements of chief executive officers (CEOs) of major corporations. He believes that the mean systolic blood pressure, μ, of CEOs of major corporations is different from 136 mm Hg, which is the value reported in a possibly outdated journal article. He plans to perform a statistical test. He measures the systolic blood pressures of a random sample of CEOs of major corporations and finds the mean of the sample to be 126 mm Hg and the standard deviation of the sample to be 18 mm Hg.Based on this information, answer the questions below.What are the null hypothesis and alternative to be used for the test (ie, less than, less than or equal to etc)H0 is μ= ____ _______( 18,136, 126) pick oneH1 is μ = _____ _____ (18,136,126) pick oneIn the context of this test what is the type I error? Pick one in the parathensisA type I error is ______(rejecting or failing to reject) that the μ is____________ (less than , equal to, etc) (18,136,126) when in fact μ is__________ ( less than, greater to , etc) (18,136,126)Suppose the researcher decides not to reject the null hypothesis. What sort of error might he be making? (type I or type II)

Answer 1

Null Hypothesis,
`H_0` :
`\mu` = 136 mm Hg

Alternate Hypothesis,
`H_A` :
`\mu\\eq` 136 mm Hg

In this context type I error is rejecting that the μ is equal to 136 mm Hg when in fact μ is equal to 136 mm Hg.

Explanation:

We are given that the mean systolic blood pressure, μ, of CEOs of major corporations is different from 136 mm Hg, which is the value reported in a possibly outdated journal article.

He measures the systolic blood pressures of a random sample of CEOs of major corporations and finds the mean of the sample to be 126 mm Hg and the standard deviation of the sample to be 18 mm Hg.

So, Null Hypothesis,
`H_0` :
`\mu` = 136 mm Hg {means that the mean systolic blood pressure, μ, of CEOs of major corporations is 136 mm Hg}

Alternate Hypothesis,
`H_A` :
`\mu\\eq` 136 mm Hg {means that the mean systolic blood pressure, μ, of CEOs of major corporations is 136 mm Hg}

Type I error states that the null hypothesis is rejected when in fact the null hypothesis was true. So, in this context type I error is rejecting that the μ is equal to 136 mm Hg when in fact μ is equal to 136 mm Hg.

Suppose the researcher decides not to reject the null hypothesis. It means the researcher is making a type I error.