MATH 225N WEEK 7 HYPOTHESIS TESTING QUESTION AND ANSWERS LATEST UPDATE 2026 RATED A+

MATH 225N WEEK 7 HYPOTHESIS TESTING QUESTION AND ANSWERS LATEST UPDATE 2026 RATED A+
• 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=0.05 we reject Ho and support the Ha
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 (≠) ±
(decimal)
(decimal)
0.05
0.5000
50
32
0.640000
0.500000
0.070711
1.979899
0.023852
0.047704
1.644854
-
1.644854
1.959964
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 = 0.5 Ha ≠ 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, 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 = ≥ 0.058 Ha ¿ 0.058 (one tailed test) n = 500 (α is not given soleave it 0.05)
Hypothesis Test for p population
0.05
0.5000
200
108
0.540000
0.500000
0.035355
1.131371
0.129238
0.258476
1.644854
-
1.644854
1.959964
proportion
Level of
Significance
Proportion under
H0
n
Number of
Successes
(decimal)
(decimal)
0.05
0.0580
500
21

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