Question
Your friend claims that he averages a 95% on his exams. You want to test his claim.
Identify the null hypothesis.
Identify the alternative hypothesis.
A hypothesis test is conducted at the 7% significance level. If the p-value is 0.049, what conclusion should be drawn?
A. You cannot conclude that your friend doesn't average a 95% on his exams.
B. You conclude that your friend doesn't average a 95% on his exams.
Identify the null hypothesis.
Identify the alternative hypothesis.
A hypothesis test is conducted at the 7% significance level. If the p-value is 0.049, what conclusion should be drawn?
A. You cannot conclude that your friend doesn't average a 95% on his exams.
B. You conclude that your friend doesn't average a 95% on his exams.
Answers
GPT-4o mini
To test your friend's claim that he averages a 95% on his exams, we set up the hypotheses as follows:
### Null Hypothesis (H0):
The null hypothesis states that your friend's average is equal to 95%.
\[ H_0: \mu = 95 \]
### Alternative Hypothesis (H1):
The alternative hypothesis states that your friend's average is not equal to 95%.
\[ H_1: \mu \neq 95 \]
This is a two-tailed test since we are interested in deviations from 95% in either direction.
### Conclusion Based on P-value:
You are conducting the hypothesis test at the 7% significance level (α = 0.07) and you obtained a p-value of 0.049.
Since the p-value (0.049) is less than the significance level (0.07), you reject the null hypothesis.
Therefore, the conclusion that should be drawn is:
**B. You conclude that your friend doesn't average a 95% on his exams.**
### Null Hypothesis (H0):
The null hypothesis states that your friend's average is equal to 95%.
\[ H_0: \mu = 95 \]
### Alternative Hypothesis (H1):
The alternative hypothesis states that your friend's average is not equal to 95%.
\[ H_1: \mu \neq 95 \]
This is a two-tailed test since we are interested in deviations from 95% in either direction.
### Conclusion Based on P-value:
You are conducting the hypothesis test at the 7% significance level (α = 0.07) and you obtained a p-value of 0.049.
Since the p-value (0.049) is less than the significance level (0.07), you reject the null hypothesis.
Therefore, the conclusion that should be drawn is:
**B. You conclude that your friend doesn't average a 95% on his exams.**
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