QUESTION 1
·
1/1 POINTS
A researcher claims that the proportion of smokers in a certain city is less than 20%. To
test this claim, a random sample of 700 people is taken in the city and 150 people
indicate they are smokers.
The following is the setup for this hypothesis test:
H0:p=0.20
Ha:p<0.20
Find the p-value for this hypothesis test for a proportion and round your answer to 3
decimal places.
The following table can be utilized which provides areas under the Standard Normal
Curve:
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.7 0.758 0.761 0.764 0.767 0.770 0.773 0.776 0.779 0.782 0.78
0.8 0.788 0.791 0.794 0.797 0.800 0.802 0.805 0.808 0.811 0.81
0.9 0.816 0.819 0.821 0.824 0.826 0.829 0.831 0.834 0.836 0.83
1.0 0.841 0.844 0.846 0.848 0.851 0.853 0.855 0.858 0.860 0.86
1.1 0.864 0.867 0.869 0.871 0.873 0.875 0.877 0.879 0.881 0.88
That is correct!
$$P-value=0.826
Answer Explanation
Correct answers:
, • $\text{P-value=}0.826\ $P-value=0.826
Here are the steps needed to calculate the p-value for a hypothesis test for a proportion:
1. Determine if the hypothesis test is left tailed, right tailed, or two tailed.
2. Compute the value of the test statistic.
3. If the hypothesis test is left tailed, the p-value will be the area under the standard
normal curve to the left of the test statistic z0
If the test is right tailed, the p-value will be the area under the standard normal
curve to the right of the test statistic z0
If the test is two tailed, the p-value will be the area to the left of −|z0| plus the
area to the right of |z0| under the standard normal curve
For this example, the test is a left tailed test and the test statistic, rounding to two
decimal places,
is z=0.2142857−0.200.20(1−0.20)700−−−−−−−−−−−−√≈0.94.
Thus the p-value is the area under the Standard Normal curve to the left of a z-score of
0.94.
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.7 0.758 0.761 0.764 0.767 0.770 0.773 0.776 0.779 0.782 0.78
0.8 0.788 0.791 0.794 0.797 0.800 0.802 0.805 0.808 0.811 0.81
0.9 0.816 0.819 0.821 0.824 0.826 0.829 0.831 0.834 0.836 0.83
1.0 0.841 0.844 0.846 0.848 0.851 0.853 0.855 0.858 0.860 0.86
1.1 0.864 0.867 0.869 0.871 0.873 0.875 0.877 0.879 0.881 0.88
From a lookup table of the area under the Standard Normal curve, the corresponding
area is then 0.826.
FEEDBACK
•
•
•
•
, Content attribution- Opens a dialog
QUESTION 2
·
1/1 POINTS
The finishing times, in minutes, for running marathons have an unknown distribution
with mean 297 and standard deviation 32 minutes. A sample, with size n=41, was
randomly drawn from the population. Using the Central Limit Theorem for Means, what
is the mean for the sample mean distribution?
Give just a number for your answer.
That is correct!
$$297
Answer Explanation
Correct answers:
• $297$297
The Central Limit Theorem for Means states that the mean of the normal distribution of
sample means is equal to the mean of the original distribution, 297.
FEEDBACK
•
•
•
•
Content attribution- Opens a dialog
QUESTION 3
·
1/1 POINTS
, According to a marketing research study, American teenagers watched 16.5 hours
of social media posts per month last year, on average. A random sample
of 20 American teenagers was surveyed and the mean amount of time per month each
teenager watched social media posts was 17.3. This data has a sample standard
deviation of 2.1. (Assume that the scores are normally distributed.)
Researchers conduct a one-mean hypothesis at the 10% significance level to test if the
mean amount of time American teenagers watch social media posts per month is
greater than the mean amount of time last year.
Which answer choice shows the correct null and alternative hypotheses for this test?
That is correct!
H0:μ=17.3; Ha:μ<17.3, which is a left-tailed test.
H0:μ=17.3; Ha:μ>17.3, which is a right-tailed test.
H0:μ=16.5; Ha:μ<16.5, which is a left-tailed test.
H0:μ=16.5; Ha:μ>16.5, which is a right-tailed test.
Answer Explanation
Correct answer:
H0:μ=16.5; Ha:μ>16.5, which is a right-tailed test.
The null hypothesis should be the mean amount of time last year: H0:μ=16.5. The
study wants to know if the amount of time American teenagers watch social media
posts per month is greater than 16.5 hours now. This means that we just want to test if
the mean is greater than 16.5 hours now. So, the alternative hypothesis is Ha:μ>16.5,
which is a right-tailed test.
FEEDBACK
•
•
·
1/1 POINTS
A researcher claims that the proportion of smokers in a certain city is less than 20%. To
test this claim, a random sample of 700 people is taken in the city and 150 people
indicate they are smokers.
The following is the setup for this hypothesis test:
H0:p=0.20
Ha:p<0.20
Find the p-value for this hypothesis test for a proportion and round your answer to 3
decimal places.
The following table can be utilized which provides areas under the Standard Normal
Curve:
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.7 0.758 0.761 0.764 0.767 0.770 0.773 0.776 0.779 0.782 0.78
0.8 0.788 0.791 0.794 0.797 0.800 0.802 0.805 0.808 0.811 0.81
0.9 0.816 0.819 0.821 0.824 0.826 0.829 0.831 0.834 0.836 0.83
1.0 0.841 0.844 0.846 0.848 0.851 0.853 0.855 0.858 0.860 0.86
1.1 0.864 0.867 0.869 0.871 0.873 0.875 0.877 0.879 0.881 0.88
That is correct!
$$P-value=0.826
Answer Explanation
Correct answers:
, • $\text{P-value=}0.826\ $P-value=0.826
Here are the steps needed to calculate the p-value for a hypothesis test for a proportion:
1. Determine if the hypothesis test is left tailed, right tailed, or two tailed.
2. Compute the value of the test statistic.
3. If the hypothesis test is left tailed, the p-value will be the area under the standard
normal curve to the left of the test statistic z0
If the test is right tailed, the p-value will be the area under the standard normal
curve to the right of the test statistic z0
If the test is two tailed, the p-value will be the area to the left of −|z0| plus the
area to the right of |z0| under the standard normal curve
For this example, the test is a left tailed test and the test statistic, rounding to two
decimal places,
is z=0.2142857−0.200.20(1−0.20)700−−−−−−−−−−−−√≈0.94.
Thus the p-value is the area under the Standard Normal curve to the left of a z-score of
0.94.
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.7 0.758 0.761 0.764 0.767 0.770 0.773 0.776 0.779 0.782 0.78
0.8 0.788 0.791 0.794 0.797 0.800 0.802 0.805 0.808 0.811 0.81
0.9 0.816 0.819 0.821 0.824 0.826 0.829 0.831 0.834 0.836 0.83
1.0 0.841 0.844 0.846 0.848 0.851 0.853 0.855 0.858 0.860 0.86
1.1 0.864 0.867 0.869 0.871 0.873 0.875 0.877 0.879 0.881 0.88
From a lookup table of the area under the Standard Normal curve, the corresponding
area is then 0.826.
FEEDBACK
•
•
•
•
, Content attribution- Opens a dialog
QUESTION 2
·
1/1 POINTS
The finishing times, in minutes, for running marathons have an unknown distribution
with mean 297 and standard deviation 32 minutes. A sample, with size n=41, was
randomly drawn from the population. Using the Central Limit Theorem for Means, what
is the mean for the sample mean distribution?
Give just a number for your answer.
That is correct!
$$297
Answer Explanation
Correct answers:
• $297$297
The Central Limit Theorem for Means states that the mean of the normal distribution of
sample means is equal to the mean of the original distribution, 297.
FEEDBACK
•
•
•
•
Content attribution- Opens a dialog
QUESTION 3
·
1/1 POINTS
, According to a marketing research study, American teenagers watched 16.5 hours
of social media posts per month last year, on average. A random sample
of 20 American teenagers was surveyed and the mean amount of time per month each
teenager watched social media posts was 17.3. This data has a sample standard
deviation of 2.1. (Assume that the scores are normally distributed.)
Researchers conduct a one-mean hypothesis at the 10% significance level to test if the
mean amount of time American teenagers watch social media posts per month is
greater than the mean amount of time last year.
Which answer choice shows the correct null and alternative hypotheses for this test?
That is correct!
H0:μ=17.3; Ha:μ<17.3, which is a left-tailed test.
H0:μ=17.3; Ha:μ>17.3, which is a right-tailed test.
H0:μ=16.5; Ha:μ<16.5, which is a left-tailed test.
H0:μ=16.5; Ha:μ>16.5, which is a right-tailed test.
Answer Explanation
Correct answer:
H0:μ=16.5; Ha:μ>16.5, which is a right-tailed test.
The null hypothesis should be the mean amount of time last year: H0:μ=16.5. The
study wants to know if the amount of time American teenagers watch social media
posts per month is greater than 16.5 hours now. This means that we just want to test if
the mean is greater than 16.5 hours now. So, the alternative hypothesis is Ha:μ>16.5,
which is a right-tailed test.
FEEDBACK
•
•
