Chapter 8, Problem 7P

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8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

A random sample of *n* = 25 scores is selected from a normal population with a mean of
*M* = 44.

**a.** If the population standard deviation is

**b.** If the population standard deviation is

**c.** Comparing your answers for parts a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.

**a.**

To determine

The sample mean sufficient to conclude that the treatment has a significant effect if the population standard deviation is
σ = 5 .

Explanation

**Given info:**

Samples mean (*M*) is 44, population mean is 40, standard deviation is 5, alpha level is 0.05 and sample size is 25.

**Justification:**

The null hypothesis states that there is no effect of the treatment and alternative hypothesis states opposite of null hypothesis. As given in the question that population mean is 40 and two tailed test is used, so the null hypothesis and alternative hypothesis for this question are:

The alpha level is given in the question as 0.05 and need to find boundaries of the critical region. As given in the question that two tailed hypothesis test used, so acceptance region is:

The z-score critical value at 0.975 or at

**b.**

To determine

The sample mean sufficient to conclude that the treatment has a significant effect if the population standard deviation is
σ = 15 .

**c.**

To determine

**To explain:** The change in magnitude of the standard deviation influences the outcome of a hypothesis test.

Sect-8.1 P-1LCSect-8.1 P-2LCSect-8.1 P-3LCSect-8.1 P-1LCASect-8.1 P-2LCASect-8.1 P-3LCASect-8.2 P-1LCSect-8.2 P-2LCSect-8.2 P-3LCSect-8.2 P-4LC

Sect-8.2 P-5LCSect-8.3 P-1LCSect-8.3 P-2LCSect-8.3 P-3LCSect-8.3 P-4LCSect-8.3 P-5LCSect-8.4 P-1LCSect-8.4 P-2LCSect-8.4 P-3LCSect-8.5 P-1LCSect-8.5 P-2LCSect-8.5 P-3LCSect-8.6 P-1LCSect-8.6 P-2LCSect-8.6 P-3LCSect-8.6 P-4LCCh-8 P-1PCh-8 P-2PCh-8 P-3PCh-8 P-4PCh-8 P-5PCh-8 P-6PCh-8 P-7PCh-8 P-8PCh-8 P-9PCh-8 P-10PCh-8 P-11PCh-8 P-12PCh-8 P-13PCh-8 P-14PCh-8 P-15PCh-8 P-16PCh-8 P-17PCh-8 P-18PCh-8 P-19PCh-8 P-20PCh-8 P-21PCh-8 P-1RECh-8 P-2RECh-8 P-3RE

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