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