MATH 225N Week 7 Hypothesis Testing Question and Answers Steve listens to his favorite streaming music service when he works out. He wonders whether the service 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 b...
lOMoARcPSD|3013804
MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+lOMoARcPSD|3013804
Steve listens to his favorite streaming music service when he works out. He wonders whether the service
algorithm does a good job of finding random songs that he will like often. 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 than not and then draw a conclusion
in the context of a problem. Use α = 0.05. Type equation here .
Ho: p =≤ 0.5(50%) p = 0.5
Ha: p = > 0.5 (strictly¿>≠)
P-value = 0.02 which is <α =0.05we reject Ho and support the Ha
Hypothesis Test for p population proportion
Level of
Significance
Proportion
under(decimal)
(decimal)
H0
n
Number of
Successes
Sample Proportion
StDev
SE
Test Statistic (z)
One-Sided p-value
Two-Sided p-value
Right-Tailed (>)
Left-Tailed (<)
Two-Tailed (≠) ±0.05
0.5000
50
32
0.640000
0.500000
0.070711
1.979899
0.023852
0.047704
1.644854
- 1.644854
1.959964 lOMoARcPSD|3013804
MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+
Answer: Reject the null hypothesis. There is sufficient evidence to prove that Steve will like a random selected song more often than not.
A magazine regularly tested products and gave the reviews to its customers. In one of its reviews, it tested 2 types of batteries and claimed that the batteries from company A outperformed batteries from company B in 108 of the tests. There were 200 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 it to 3 decimal places.
Ho: p = 0.5Ha≠ 0.5(two tailed test) n = 200(α is not given soleave it 0.05)
Hypothesis Test for p population proportion
Level of
Significance
Proportion under
H0
n
Number of
Successes
Sample Proportion
StDev
SE
Test Statistic (z)
One-Sided p-value
Two-Sided p-value
Right-Tailed (>)
Left-Tailed (<)
Two-Tailed (≠) ±
Answer: 0.258 (because it is a two tailed test). We are not rejecting the null hypothesis and we do not have evidence to support the alternative hypothesis.
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,
MATH 225N Week 7 Hypothesis Testing Question and Answers
Latest Update 2023 Rated A+0.05
0.5000
200
108
0.540000
0.500000
0.035355
1.131371
0.129238
0.258476
1.644854
- 1.644854
1.959964 lOMoARcPSD|3013804
MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+
so she had a government official from the state randomly select 500 ballots and count how many were defective. The official found 21 defective ballots.
Use Excel to test if the candidates claim is true and that < 5.8% of the ballots were defective. Identify the p=value rounding to 3 decimal places.
Ho: p =≥ 0.058Ha¿ 0.058(one tailed test) n = 500(α is not given soleave it 0.05)
Hypothesis Test for p population proportion
Level of
Significance
Proportion under
H0
n
Number of
Successes(decimal)
(decimal)
MATH 225N Week 7 Hypothesis Testing Question and Answers
Latest Update0.05
0.0580
500
21 lOMoARcPSD|3013804
MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+
Sample Proportion
St Dev
SE
Test Statistic (z)
One-Sided p-value
Two-Sided p-value
Right Tailed (>)
Left-Tailed (<)
Two-Tailed (≠) ±
Answer: 0.063
A researcher claims that the incidence of a certain type of cancer is < 5%. To test this claim, a random sample of 4000 people are checked and 170 are found to have the cancer.
The following is the set up for the hypothesis:
Ho = 0.05 Ha = < 0.05
In the example the p-value was determined to be 0.015.
Come to a conclusion and interpret the results of this hypothesis test for a proportion (use a significance level of
5%)
Answer: The decision is to reject the null hypothesis. The conclusion is that there is enough evidence to support the claim.
A researcher is investigating a government claim that the unemployment rate is < 5%. T O
test this claim, a random sample of 1500 people is taken and it is determined that 61
people were unemployed.
Ho: p = 0.05 Ha: p < 0.05
Find the p-value for this hypothesis test for a proportion & round to 3 decimal places.
MATH 225N Week 7 Hypothesis Testing Question and Answers
Latest Update 2023 Rated A+0.04200
0
0.23374
3
0.01045
3
-
1.53061
3
0.06300
8
0.12601
6
1.644854
- 1.644854
1.959964
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