I need help with 4, 5 and 6 ### Night OwlsA MSU psychologist reports that 40% of MSU students regularly sleep less than 8 hours each night. Cindy believes that the actual proportion of MSU students who regularly sleep less than 8 hours each night is **less than** the value reported by the MSU psychologist. She randomly selects 215 students and asks them, “Do you regularly sleep less than 8 hours each night?” She finds that 77 of the 215 students answered “yes” to the question.1. **Which one of the following statements about the number 40% is correct?** - A. It is a sample statistic. - B. It is a standard error. - C. It is a margin of error. - D. It is a claimed parameter.2. **Choose the null and alternative hypotheses Cindy should use to test her theory.** - A. $ H_0 : p = 0.4, \ H_A : p \neq 0.4 $ - B. $ H_0 : p = 0.4, \ H_A : p < 0.4 $ - C. $ H_0 : p = 0.4, \ H_A : \hat{p} < 0.36 $ - D. $ H_0 : p = 0.4, \ H_A : \hat{p} > 0.4 $3. **If you assume that the observations in the sample are independent, what is the smallest value the sample size could be to meet the conditions for this hypothesis test?** - A. 28 - B. 10 - C. None of the above - D. 20 - E. 77 - F. 26 ### Calculating Test Statistics and p-value4. **Calculate the test statistic.**\[z = \_\_\_\_\_\]5. **Calculate the p-value.**\[p = \_\_\_\_\_\]6. **Which of the following describes the probability represented by the p-value for this test?**- **A.** It is the probability that any random sample of 215 MSU students would have 35.81% saying they regularly sleep less than 8 hours a day.- **B.** It is the probability that a random sample of 215 MSU students would result in 35.81% or fewer who regularly sleep less than 8 hours a day, assuming the null model is valid.- **C.** It is the probability that 40% of all MSU students regularly sleep less than 8 hours a day, assuming the null model is valid.- **D.** It is the probability that less than 40% of MSU students regularly sleep less than 8 hours a day if, in fact, 35.81% actually do.- **E.** None of the above.**Explanation:**- **Test Statistic (z):** This is a value calculated from the sample data that is used to decide whether to reject the null hypothesis. It measures the number of standard deviations the sample proportion is from the null hypothesis population proportion.- **p-value:** This represents the probability of obtaining a test statistic at least as extreme as the one computed, assuming the null hypothesis is true. It helps in assessing the significance of the results.**Choosing the Correct p-value Interpretation:**Option B is typically the correct choice, as it deals with the probability of observing a sample statistic as extreme as the one observed, under the assumption that the null hypothesis is true. **Graphical and Diagram Details:**In this context, the text does not provide any graphs or diagrams. However, if there were a graph, it might typically show a normal distribution curve illustrating the test statistic’s placement on the curve and the area under the curve corresponding to the p-value.

The random variable time follows normal distribution. The population proportion is 40%. We have to…

Night Owls - A MSU psychologist reports that 40% of MSU students regularly sleep less than 8 hours each night. Cindy believes that the actual proportion of MSU students who regularly sleep less than 8 hours each night is less than the value reported by the MSU psychologist. She randomly selects 215 students and asks them, "Do you regularly sleep less than 8 hours each night?" She finds that 77 of the 215 students answered "yes" to the question. 1. Which one of the following statements about the number 40% is correct? OA. It is a sample statistic. OB. It is a standard error. OC. It is a margin of error. OD. It is a claimed parameter. 2. Choose the null and alternative hypotheses Cindy should use to test her theory. OA. Họ : p = 0.4, HA : P + 0.4 ов. Но : р3 0.4, НА : р<0.4 ос. Но : р%3D0.4, На : р<0.36 OD. Ho : р%3 0.4, НА : р> 0.4 3. If you assume that the observations in the sample are independent, what is the smallest value the sample size could be to meet the conditions for this hypothesis test? OA. 28 ов. 10 OC. None of the above OD. 20 OE. 77 OF. 26

Night Owls - A MSU psychologist reports that 40% of MSU students regularly sleep less than 8 hours each night. Cindy believes that the actual proportion of MSU students who regularly sleep less than 8 hours each night is less than the value reported by the MSU psychologist. She randomly selects 215 students and asks them, "Do you regularly sleep less than 8 hours each night?" She finds that 77 of the 215 students answered "yes" to the question. 1. Which one of the following statements about the number 40% is correct? OA. It is a sample statistic. OB. It is a standard error. OC. It is a margin of error. OD. It is a claimed parameter. 2. Choose the null and alternative hypotheses Cindy should use to test her theory. OA. Họ : p = 0.4, HA : P + 0.4 ов. Но : р3 0.4, НА : р<0.4 ос. Но : р%3D0.4, На : р<0.36 OD. Ho : р%3 0.4, НА : р> 0.4 3. If you assume that the observations in the sample are independent, what is the smallest value the sample size could be to meet the conditions for this hypothesis test? OA. 28 ов. 10 OC. None of the above OD. 20 OE. 77 OF. 26

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

I need help with 4, 5 and 6

### Night Owls

A MSU psychologist reports that 40% of MSU students regularly sleep less than 8 hours each night. Cindy believes that the actual proportion of MSU students who regularly sleep less than 8 hours each night is **less than** the value reported by the MSU psychologist. She randomly selects 215 students and asks them, “Do you regularly sleep less than 8 hours each night?” She finds that 77 of the 215 students answered “yes” to the question.

1. **Which one of the following statements about the number 40% is correct?**

- A. It is a sample statistic.
- B. It is a standard error.
- C. It is a margin of error.
- D. It is a claimed parameter.

2. **Choose the null and alternative hypotheses Cindy should use to test her theory.**

- A. $ H_0 : p = 0.4, \ H_A : p \neq 0.4 $
- B. $ H_0 : p = 0.4, \ H_A : p < 0.4 $
- C. $ H_0 : p = 0.4, \ H_A : \hat{p} < 0.36 $
- D. $ H_0 : p = 0.4, \ H_A : \hat{p} > 0.4 $

3. **If you assume that the observations in the sample are independent, what is the smallest value the sample size could be to meet the conditions for this hypothesis test?**

- A. 28
- B. 10
- C. None of the above
- D. 20
- E. 77
- F. 26

### Calculating Test Statistics and p-value

4. **Calculate the test statistic.**

\[
z = \_\_\_\_\_
\]

5. **Calculate the p-value.**

\[
p = \_\_\_\_\_
\]

6. **Which of the following describes the probability represented by the p-value for this test?**

- **A.** It is the probability that any random sample of 215 MSU students would have 35.81% saying they regularly sleep less than 8 hours a day.
- **B.** It is the probability that a random sample of 215 MSU students would result in 35.81% or fewer who regularly sleep less than 8 hours a day, assuming the null model is valid.
- **C.** It is the probability that 40% of all MSU students regularly sleep less than 8 hours a day, assuming the null model is valid.
- **D.** It is the probability that less than 40% of MSU students regularly sleep less than 8 hours a day if, in fact, 35.81% actually do.
- **E.** None of the above.

**Explanation:**

- **Test Statistic (z):** This is a value calculated from the sample data that is used to decide whether to reject the null hypothesis. It measures the number of standard deviations the sample proportion is from the null hypothesis population proportion.
- **p-value:** This represents the probability of obtaining a test statistic at least as extreme as the one computed, assuming the null hypothesis is true. It helps in assessing the significance of the results.

**Choosing the Correct p-value Interpretation:**

Option B is typically the correct choice, as it deals with the probability of observing a sample statistic as extreme as the one observed, under the assumption that the null hypothesis is true.

**Graphical and Diagram Details:**

In this context, the text does not provide any graphs or diagrams. However, if there were a graph, it might typically show a normal distribution curve illustrating the test statistic’s placement on the curve and the area under the curve corresponding to the p-value.

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