allison randomly sampled 40 students in a particular class and asked each how many hours per week they studied. she calculated a sample mean, $ \bar{x} $ of 9.5 hours per week. her hypotheses were $ h_{0}: \mu_{x}=8 $ hours per week and $ h_{a}: \mu_{x}8 $ hours per week, where $ x $ is the number of hours students spent studying per week. she performed a hypothesis test and obtained a p - value of 0.0003. what does this mean? select all that apply. a. the probability that the mean number of hours spent studying per week for all students in this class is 8 hours per week is 0.0003. b. the probability that the true mean number of hours spent studying per week for all students in this class is 9.5 hours or more is 0.0003. c. the probability that the mean number of hours spent studying per week for all students in this class is more than 8 hours per week is 0.0003. d. of all the random samples of 40 students from this class, 0.03% would give a sample mean of 9.5 hours per week or more given that the true mean number of hours spent studying for this class for all students in the class is 8 hours per week

Question

allison randomly sampled 40 students in a particular class and asked each how many hours per week they studied. she calculated a sample mean, $ \bar{x} $ of 9.5 hours per week. her hypotheses were $ h_{0}: \mu_{x}=8 $ hours per week and $ h_{a}: \mu_{x}>8 $ hours per week, where $ x $ is the number of hours students spent studying per week. she performed a hypothesis test and obtained a p - value of 0.0003. what does this mean? select all that apply. a. the probability that the mean number of hours spent studying per week for all students in this class is 8 hours per week is 0.0003. b. the probability that the true mean number of hours spent studying per week for all students in this class is 9.5 hours or more is 0.0003. c. the probability that the mean number of hours spent studying per week for all students in this class is more than 8 hours per week is 0.0003. d. of all the random samples of 40 students from this class, 0.03% would give a sample mean of 9.5 hours per week or more given that the true mean number of hours spent studying for this class for all students in the class is 8 hours per week

Accepted Answer

# Explanation:
## Step1: Understand the concept of p - value
The p - value is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis $H_0$ is true.

## Step2: Analyze each option
- **Option A**: The p - value is not the probability that the null hypothesis ($\mu_x = 8$) is true. The p - value is calculated under the assumption that $H_0$ is true. So, this option is incorrect.
- **Option B**: The p - value is not about the probability of the sample mean. It is about the probability of getting a sample result (or more extreme) given the null hypothesis. So, this option is incorrect.
- **Option C**: The p - value is not the probability that the alternative hypothesis ($\mu_x>8$) is true. It is calculated under the null - hypothesis assumption. So, this option is incorrect.
- **Option D**: Since $0.0003=\frac{0.03}{100}$, the p - value of $0.0003$ means that if the null hypothesis ($\mu_x = 8$) is true, then $0.03\%$ of all random samples of $n = 40$ students would give a sample mean of $\bar{x}=9.5$ hours per week or more. This is the correct interpretation of the p - value.

# Answer:
D. Of all the random samples of 40 students from this class, 0.03% would give a sample mean of 9.5 hours per week or more given that the true mean number of hours spent studying for this class for all students in the class is 8 hours per week.

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Question

Explanation:

Step1: Understand the concept of p - value

Step2: Analyze each option

Answer: