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**

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= 20. The sample of n = 25 students
had a mean score of M = 80. Can we conclude...

Some researchers claim that herbal supplements such as ginseng
or ginkgo biloba enhance human memory. To test this claim, a
researcher selects a sample of n = 25 college students. Each
student is given a ginkgo biloba supplement daily for six weeks and
then all the participants are given a standardized memory test. For
the population, scores on the test are normally distributed with m
= 70 and s = 15. The sample of n = 25 students had a...

Some researchers claim that herbal supplements like ginseng
enhance human memory. To test this claim, a researcher selects a
sample of n=30 college students. Each student is given a
ginseng supplement daily for six weeks and then all of the
participants are given a standard memory test. For the population,
scores on the test are normally distributed with μ=80 and σ=20. The
sample of n=30 students had a mean memory score of
M=85.
a) Are these data sufficient to show...

Some researchers claim that herbal supplements such as ginseng
or ginkgo biloba enhance human memory. To test this claim, a
researcher selects a sample of n = 28 college students. Each
student is given a ginkgo biloba supplement daily for 6 weeks and
then all of the participants are given a standardized memory test.
Scores on the standardized test are μ = 80 and standard
deviation of 15. The sample of 28 students had a mean score of M =...

Some researchers claim that herbal supplements such as ginseng
or ginkgo biloba enhance human memory. To test this claim, a
researcher selects a sample of n = 28 college students. Each
student is given a ginkgo biloba supplement daily for 6 weeks and
then all of the participants are given a standardized memory test.
Scores on the standardized test are μ = 80 and standard deviation
of 15. The sample of 28 students had a mean score of M =...

A researcher is testing the effectiveness of a new herbal
supplement that claims to improve memory performance. A
sample of n = 25 college students is obtained and each student
takes the supplement daily for six week. At the end of
the 6-week period, each student is given a standardized memory test
and the average score for the sample is M = 39. For the
general population of college students, the distribution of test
scores is normal with a mean of µ =...

You wish to test the
claim that the average IQ score is less than 100 at the .005
significance level. You determine the hypotheses are:
Ho: μ=100
H1:μ<100
You take a simple
random sample of 76 individuals and find the mean IQ score is 95.5,
with a standard deviation of 15.1. Let's consider testing this
hypothesis two ways: once with assuming the population standard
deviation is not known and once with assuming that it is known.
Round to three decimal...

Test the claim about the population mean μ at the level of
significance α. Assume the population is normally distributed.
Write out null and alternative hypotheses, your critical z-score
and your z-test statistic. Decide whether you would reject or fail
to reject your null hypothesis.
Claim: μ > 28; α = 0.05, σ = 1.2
Sample statistics: x̅ = 28.3, n = 50
H0:
Ha:
Critical z-score:
Z test statistic:
Decision:

Many people take ginkgo supplements advertised to improve
memory. Are these over-the-counter supplements effective? In a
study reported in the paper “Ginkgo for memory Enhancement”
(Journal of the American Medical Association), elderly
adults were assigned at random to either a treatment or a control
group. The 104 participants who were assigned to the treatment
group took 40 mg of ginkgo three times a day for six weeks. The 115
participants assigned to the control group took a placebo pill
three...

You wish to test the following claim (H1) at a significance
level of α=0.01.
Ho:μ=82.6
H1:μ>82.6
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain the following sample of
data:
data
84.2
79.3
95
87.8
81.6
86.2
82.9
112.6
102.1
85
96.7
67.3
What is the critical value for this test? (Report answer accurate
to three decimal places.)
critical value =
What is the test statistic for this sample? (Report answer accurate...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago