Week 7 Assignment Hypothesis Test for the mean-Polution Standard Deviation known
Compute the value of the test statistic (z-value) for a hypothesis test for one population mean with a
known standard deviation
Question
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Week 7 Assignment Hypothesis Test for the mean-Polution Standard Deviation known
Compute the value of the test statistic (z-value) for a hypothesis test for one population mean with a
known standard deviation
Question
Jamie, a bowler, claims that her bowling score is less than 168 points, on average.
Several of her teammates do not believe her, so she decides to do a hypothesis
test, at a 1% significance level, to persuade them. She bowls 17 games. The mean
score of the sample games is 155 points. Jamie knows from experience that the
standard deviation for her bowling score is 19 points.
H0: μ≥168; Ha: μ<168
α=0.01 (significance level)
What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two
decimal places?
Provide your answer: Test statistic = -2.82
Correct answers:
Test statistic = −2.82
The hypotheses were chosen, and the significance level was decided on, so the next
step in hypothesis testing is to compute the test statistic. In this scenario, the
sample mean score, x¯=155. The sample the bowler uses is 17 games,
so n=17. She knows the standard deviation of the games, σ=19. Lastly, the
bowler is comparing the population mean score to 168points. So, this value
(found in the null and alternative hypotheses) is μ0. Now we will substitute the
values into the formula to compute the test statistic:
z0=x¯−μ0σn√=155−1681917√≈−134.608≈−2.82
So, the test statistic for this hypothesis test is z0=−2.82.
Distinguish between one- and two-tailed hypotheses tests and understand possible conclusions
Question
Which graph below corresponds to the following hypothesis test?
H0:μ≥5.9, Ha:μ<5.9
Answer ExplanationCorrect answer:
A normal curve is over a horizontal axis and is centered on 5.9. A vertical line
segment extends from the horizontal axis to the curve at a point to the left of 5.9.
The area under the curve to the left of the point is shaded.
The alternative hypothesis, Ha, tells us which area of the graph we are interested
in. Because the alternative hypothesis is μ<5.9, we are interested in the
region less than (to the left of) 5.9, so the correct graph is the first answer choice.
Your answer: wrong
Identify the null and alternative hypotheses
Question
A politician claims that at least 68% of voters support a decrease in taxes. A group
of researchers are trying to show that this is not the case. Identify the researchers'
null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the
parameter p.
Select the correct answer below:
H0: p≤0.68; Ha: p>0.68
H0: p<0.68; Ha: p≥0.68
H0: p>0.68; Ha: p≤0.68
H0: p≥0.68; Ha: p<0.68Perform and interpret a hypothesis test for a proportion using Technology - Excel
Question
Steve listens to his favorite streaming music service when he works out. He
wonders whether the service's algorithm does a good job of finding random songs
that he will like more often than not. To test this, he listens to 50 songs chosen by
the service at random and finds that he likes 32 of them.
Use Excel to test whether Steve will like a randomly selected song more often than
not, and then draw a conclusion in the context of the problem. Use α=0.05.
Select the correct answer below:
Reject the null hypothesis. There is sufficient evidence to conclude that Steve will
like a randomly selected song more often than not.
Reject the null hypothesis. There is insufficient evidence to conclude that Steve will
like a randomly selected song more often than not.
Fail to reject the null hypothesis. There is sufficient evidence to conclude that Steve
will like a randomly selected song more often than not.
Fail to reject the null hypothesis. There is insufficient evidence to conclude that
Steve will like a randomly selected song more often than not.
Great work! That's correct. Correct answer:
Reject the null hypothesis. There is sufficient evidence to conclude that Steve will
like a randomly selected song more often than not.
Step 1: The sample proportion is pˆ=3250=0.64, the hypothesized proportion
is p0=0.5, and the sample size is n=50.
Step 2: The test statistic, rounding to two decimal places,
is z=0.64−0.50.5(1−0.5)50‾‾‾‾‾‾‾‾‾‾‾‾√≈1.98.
Step 3: Since the test is right-tailed, entering the
function =1−Norm.S.Dist(1.98,1) into Excel returns a p-value, rounding to three
decimal places, of 0.024.
Step 4: Since the p-value is less than α=0.05, reject the null hypothesis. There is
sufficient evidence to conclude that Steve will like a randomly selected song more
often than not.
Null and alternative hypothesis:
H0: p = 0.5
Ha: p >= 0.5Level of Significance =0.05
Proportion under H0 = 0.5
n = 50
Number of Successes=32
Sample Proportion
0.64000
StDev
0.50000
SE
0.070711
Test Statistic (z)
1.979899
One-Sided p-value
0.023852
Two-Sided p-value
0.047704
P value = 0.02 < alpha (0.05)
Hence, reject the null hypothesis.
Perform and interpret a hypothesis test for a proportion using Technology - Excel
Question
A magazine regularly tested products and gave the reviews to its customers. In one
of its reviews, it tested two types of batteries and claimed that the batteries from
Company A outperformed the batteries from Company B. A representative from
Company B asked for the exact data from the study. The author of the article told
the representative from Company B that in 200 tests, a battery from Company A
outperformed a battery from Company B in 108 of the tests. Company B decided
to sue the magazine, claiming that the results were not significantly different
from 50% and that the magazine was slandering its good name.
Use Excel to test whether the true proportion of times that Company A's batteries
outperformed Company B's batteries is different from 0.5. Identify the p-value,
rounding to three decimal places.Provide your answer below:
0.258 p-value= Well done! You got it right. Correct answers:
p-value=0.258
Step 1: The sample proportion is pˆ=108200=0.54, the hypothesized
proportion is p0=0.5, and the sample size is n=200.
Step 2: The test statistic, rounding to two decimal places,
is z=0.54−0.50.5(1−0.5)200‾‾‾‾‾‾‾‾‾‾‾‾√≈1.13.
Step 3: Since the test is two-tailed and the test statistic is positive, entering the
function =2∗(1−Norm.S.Dist(1.13,1)) into Excel returns a p-value, rounding to
three decimal places, of 0.258.
Perform and interpret a hypothesis test for a proportion using Technology - Excel
Question
A candidate in an election lost by 5.8% of the vote. The candidate sued the state
and said that more than 5.8% of the ballots were defective and not counted by
the voting machine, so a full recount would need to be done. His opponent wanted
to ask for the case to be dismissed, so she had a government official from the state
randomly select 500 ballots and count how many were defective. The
official found 45 defective ballots.
Use Excel to test if the candidate's claim is true and that more than 5.8% of the
ballots were defective. Identify the p-value, rounding to three decimal places.
Well done! You got it right. Correct answers:
p-value=0.001
Step 1: The sample proportion is pˆ=45500=0.09, the hypothesized
proportion is p0=0.058, and the sample size is n=500.
Step 2: The test statistic, rounding to two decimal places,
is z=0.09−0.0580.058(1−0.058)500‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√≈3.06.Step 3: Since the test is right-tailed, enter the function =Norm.S.Dist(3.06,0) into
Excel and subtract from 1. This returns a p-value, rounding to three decimal places,
of 0.001
Perform and interpret a hypothesis test for a proportion using Technology - Excel
Question
Dmitry suspected that his friend is using a weighted die for board games. To test
his theory, he wants to see whether the proportion of odd numbers is different
from 50%. He rolled the die 40 times and got an odd number 14 times.
Dmitry conducts a one-proportion hypothesis test at the 5% significance level, to
test whether the true proportion of odds is different from 50%.
(a) Which answer choice shows the correct null and alternative hypotheses for this
test?
Select the correct answer below:
H0:p=0.35; Ha:p>0.35, which is a right-tailed test.
H0:p=0.5; Ha:p<0.5, which is a left-tailed test.
H0:p=0.35; Ha:p≠0.35, which is a two-tailed test.
H0:p=0.5; Ha:p≠0.5, which is a two-tailed test.
Well done! You got it right.
Correct answer:
H0:p=0.5; Ha:p≠0.5, which is a two-tailed test.
The null hypothesis should be true proportion: H0:p=0.5. Dmitry wants to know
if the true proportion is different from 0.5. This means that we just want to test if
the proportion is not 0.5. So, the alternative hypothesis is Ha:p≠0.5, which is a
two-tailed test.
PART 2
Perform and interpret a hypothesis test for a proportion using Technology - Excel
Question
Dmitry suspects that his friend is using a weighted die for board games. To test his
theory, he wants to see whether the proportion of odd numbers is different from 50%.
He rolled the die 40 times and got an odd number 14 times.Dmitry conducts a one-proportion hypothesis test at the 5% significance level, to test
whether the true proportion of odds is different from 50%.
(a) H0:p=0.5; Ha:p≠0.5, which is a two-tailed test.
(b) Use Excel to test whether the true proportion of odds is different
from 50%. Identify the test statistic, z, and p-value from the Excel output,
rounding to three decimal places.
test statistic=-1.897 p-value=0.058
PART 3
Perform and interpret a hypothesis test for a proportion using Technology - Excel
Question
Dmitry suspects that his friend is using a weighted die for board games. To test his
theory, he wants to see whether the proportion of odd numbers is different from 50%.
He rolled the die 40 times and got an odd number 14 times.
Dmitry conducts a one-proportion hypothesis test at the 5% significance level, to test
whether the true proportion of odds is different from 50%.
(a) H0:p=0.5; Ha:p≠0.5, which is a two-tailed test.
(b) z0=−1.897, p-value is = 0.058
(c) Which of the following are appropriate conclusions for this hypothesis test?
Select all that apply.
Select all that apply:
We reject H0.
We fail to reject H0.
At the 5% significance level, the data provide sufficient evidence to conclude
the true proportion of odds is different than 50%.
At the 5% significance level, the data do not provide sufficient evidence to
conclude the true proportion of odds is different than 50%.
option 2 and 4 are answer
Explanation:
(c) From part b, p-value is = 0.058 > 0.05 significance level
So, we failed to reject the null hypothesis Ho
And
At the 5% significance level, the data do not provide sufficient evidence to
conclude the true proportion of odds is different than 50%.
Identify the null and alternative hypotheses
Question
A politician claims that at least 68% of voters support a decrease in taxes. A group
of researchers are trying to show that this is not the case. Identify the researchers'
null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the
parameter p.
Select the correct answer below:
H0: p≤0.68; Ha: p>0.68
H0: p<0.68; Ha: p≥0.68
H0: p>0.68; Ha: p≤0.68
H0: p≥0.68; Ha: p<0.68
4-H0: p≥0.68; Ha: p<0.68
Explanation:
First, the equal condition is written in the null hypothesis.
Second, the statement that at least 68% of taxes support a decrease in taxes is
expressed as:
H0:P≥0.68
second, the alternative hypothesis is the investigation hypothesis, the opposite
of the null hypothesis:
Ha:P<0.68
Third, therefore, the hypotheses are
H0:P≥0.68 ; Ha:P<0.68
Well done! You got it right. Let the parameter p be used to represent the
proportion. The null hypothesis is always stated with some form of equality: equal
(=), greater than or equal to (≥), or less than or equal to (≤). Therefore, in this
case, the null hypothesis H0 is p≥0.68. The alternative hypothesis is
contradictory to the null hypothesis, so Hais p<0.68.
Also, remember that the alternative hypothesis is the statement that the
research or study is trying to show. In this case, they are trying to show that the
politician is wrong, so the alternative hypothesis is the opposite of what thepolitician said. So Ha is p<0.68. The null hypothesis is what the politician said,
so H0 is p≥0.68.
Differentiate between Type I and Type II errors when performing a hypothesis test
Question
Determine the Type II error if the null hypothesis, H0, is: a wooden ladder can
withstand weights of 250pounds and less
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