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Answer :
The number 3.01 is a statistic, the symbol for the number 3.01 is μ_hat; and To conduct a simulation-based test of significance, we need to compare the observed mean (3.01 hours) with the hypothesized mean (2.75 hours).
The number 3.01 is a statistic.
The symbol for the mean number of hours per day spent watching TV for the sample of 100 Cal Poly students is μ_hat.
To conduct a simulation-based test of significance, we need to compare the observed mean (3.01 hours) with the hypothesized mean (2.75 hours). The null hypothesis is that the population mean (μ) is equal to 2.75 hours, and the alternative hypothesis is that the population mean is not equal to 2.75 hours.
Steps to find p-value:
1. Calculate the difference between the observed mean and the hypothesized mean: d = μ_hat - 2.75 hours
2. Generate a large number of random samples with the same sample size as the original sample, and calculate the mean of each sample.
3. Calculate the difference between the mean of each sample and the hypothesized mean and store the values in a list.
4. Count the number of differences that are equal to or greater than the difference between the observed mean and the hypothesized mean (d).
5. Divide the count by the total number of simulations to get the p-value. This gives us the probability of getting a sample mean equal to or greater than the observed mean if the null hypothesis is true.
6. Compare the p-value with the significance level (α) to determine whether to reject or fail to reject the null hypothesis. If the p-value is less than α, we reject the null hypothesis and conclude that the data provide evidence that the average number of hours per day Cal Poly students spending the time watching TV is different from 2.75 hours.
If the p-value is greater than α, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the average number of hours per day Cal Poly students spending the time watching TV is different from 2.75 hours.
To know more about simulation, here
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--The given question is incomplete; the complete question is
"Reconsider Dr Sameer's research question about how much time Cal Poly students spend watching television. Suppose that Dr Sameer surveys a random sample of 100 Cal Poly students, and for this sample, the mean number of hours per day spent watching TV turns out to be 3.01 hours.
1. Is the number 3.01 a parameter or a statistic?
2. Assign an appropriate symbol to the number 3.01.
3. Describe how you can conduct a simulation‐based test of significance to investigate whether the data provide evidence that the average number of hours per day Cal Poly students spend watching TV is different from 2.75 hours. Be sure to provide details on how one would find a p‐value."--
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