Question

Some researchers claim that herbal supplements improve human
memory. To test this claim, a researcher selects a sample of n = 25
college students. Each student is given herbal supplements daily
for 6 weeks and then all the participants are given a standardized
memory test. For the population, scores on the tests are normally
distributed with µ = 70 and σ= 15. The sample of n = 25 students
had a mean score of M = 75. Can we conclude that the memory scores
of the sample after the “herbal supplement” treatment are
significantly greater than those of the general
population(population mean before treatment)? **Perform a
hypothesis test using a z- score statistic. Use a one-tailed test
with α = .01**.

A) The alternative hypothesis in symbols is

H1: µ ≤ 70

H1: µ = 70

H1: µ > 70

H1: µ ≠ 7

B)The critical z-value is

1.96

1.64

2.58

2.33

C) The z-score statistic is

3

1.66

-3

2.58

D) Which of the following is the correct decision for this hypothesis test:

Reject the null hypothesis because the z-score statistic is greater than the critical z value

Fail to reject the null hypothesis because the z-score statistic is greater than the critical z value

Reject the null hypothesis because the z- score statistic is not greater than the critical z value

Fail to reject the null hypothesis because your z-score statistic is not greater than your critical z value

Answer #1

Solution:

Given ,

µ = 70 ..population mean

σ= 15 ...population SD

n = 25 ....sample size

M = 75 .....sample mean

Use α = 0.01 ...significance level

Claim: the memory scores of the sample after the “herbal supplement” treatment are significantly greater than those of the general population

i.e. µ > 70

Hypothesis are

H0 : = 70 (null hypo.)

H1 : > 70 (alternative hypothesis)

A)The alternative hypothesis in symbols is

**Answer : H1: µ > 70**

B)The critical z-value

observe that ,there is > sign in H1. So , the test is right tailed.

So the critical value is
i.e.
_{0.01}

i.e. 2.33 (Use z table to find this value)

**Answer : 2.33**

C)

The test statistic z is given by

z = (M - µ) / (σ/n)

= (75 - 70) / (15/25)

= 1.66

**Answer: 1.66**

D)Critical region is z > i.e. z > 2.33

Here , z = 1.66 is not less than = 2.33

Fail to reject the null hypothesis .

Which of the following is the correct decision for this hypothesis test:

**Fail to reject the null hypothesis because your z-score
statistic is not greater than your critical z value**

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