The population (in thousands) of 16 cities is given. This is a small sample from the bigger population of all cities in a country. в МP Арplet mp Distributions Population Quantiles Summary Statistics Mean Std Dev 100.0% maximum 1000 815.6875 99.5% 1000 110.08222 97.5% 1000 Std Err Mean 27.520556 Upper 95% Mean 874.34618 Lower 95% Mean 757.02882 90.0% 965 75.0% quartile 898.75 50.0% median 827.5 N 16 25.0% quartile 716.25 10.0% 800 700 800 000 635 600 1000 2.5% 0.5% 600 600 0.0% minimum Click here to access the JMP applet in a new window. O (a) Based on the distribution of the sample, which of the following are correct? (Select all that apply.) O Since the data is almost normal, a t-test is appropriate. O A t-test is appropriate since the population standard deviation is given. O A t-test is appropriate since the sample size is smaller than 30. O A t-test is appropriate since the population standard deviation is not known. O A z-test is appropriate since the sample standard deviation is given. There are 16 degrees of freedom. O There are 15 degrees of freedom. O A z-test is appropriate since the sample size is smaller than 30.

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The population (in thousands) of 16 cities is given. This is a small sample from the bigger population of all cities in a country.

**JMP Applet**

- **Graph Explanation:** 
  - The graph is a histogram showing the distribution of population sizes (in thousands) for 16 cities. Population values are plotted on the x-axis, and frequency is on the y-axis. The histogram shows a roughly normal distribution with a peak around 800, and it includes a box plot above the bars indicating the interquartile range and median.

**Quantiles:**
- Maximum: 1000
- 99.5%: 1000
- 97.5%: 970
- 90.0%: 965
- Upper quartile (75.0%): 898.75
- Median (50.0%): 827.5
- Lower quartile (25.0%): 716.25
- 10.0%: 635
- 2.5%: 600
- Minimum: 600

**Summary Statistics:**
- Mean: 815.6875
- Standard Deviation (Std Dev): 110.08222
- Standard Error Mean (Std Err Mean): 27.520556
- Upper 95% Mean: 874.34618
- Lower 95% Mean: 757.02882
- Sample Size (N): 16

*Click here to access the JMP applet in a new window.*

**Question (a):**

Based on the distribution of the sample, which of the following are correct? (Select all that apply.)
- □ Since the data is almost normal, a t-test is appropriate.
- □ A t-test is appropriate since the population standard deviation is given.
- □ A t-test is appropriate since the sample size is smaller than 30.
- □ A t-test is appropriate since the population standard deviation is not known.
- □ A z-test is appropriate since the sample standard deviation is given.
- □ There are 16 degrees of freedom.
- □ There are 15 degrees of freedom.
- □ A z-test is appropriate since the sample size is smaller than 30.
Transcribed Image Text:The population (in thousands) of 16 cities is given. This is a small sample from the bigger population of all cities in a country. **JMP Applet** - **Graph Explanation:** - The graph is a histogram showing the distribution of population sizes (in thousands) for 16 cities. Population values are plotted on the x-axis, and frequency is on the y-axis. The histogram shows a roughly normal distribution with a peak around 800, and it includes a box plot above the bars indicating the interquartile range and median. **Quantiles:** - Maximum: 1000 - 99.5%: 1000 - 97.5%: 970 - 90.0%: 965 - Upper quartile (75.0%): 898.75 - Median (50.0%): 827.5 - Lower quartile (25.0%): 716.25 - 10.0%: 635 - 2.5%: 600 - Minimum: 600 **Summary Statistics:** - Mean: 815.6875 - Standard Deviation (Std Dev): 110.08222 - Standard Error Mean (Std Err Mean): 27.520556 - Upper 95% Mean: 874.34618 - Lower 95% Mean: 757.02882 - Sample Size (N): 16 *Click here to access the JMP applet in a new window.* **Question (a):** Based on the distribution of the sample, which of the following are correct? (Select all that apply.) - □ Since the data is almost normal, a t-test is appropriate. - □ A t-test is appropriate since the population standard deviation is given. - □ A t-test is appropriate since the sample size is smaller than 30. - □ A t-test is appropriate since the population standard deviation is not known. - □ A z-test is appropriate since the sample standard deviation is given. - □ There are 16 degrees of freedom. - □ There are 15 degrees of freedom. - □ A z-test is appropriate since the sample size is smaller than 30.
**Determine the correct critical value of the t-distribution for α = 0.05. (Assume a one-sided test.)**

- ○ 1.341
- ○ 1.753
- ○ 2.345
- ○ 2.947
- ○ 3.733

**Should you reject or fail to reject the null hypothesis, or is there not enough information to decide? A sample statistic is tested with α = 0.05, and the corresponding t-value is 1.8 for this sample.**

- ○ Reject the null hypothesis.
- ○ Fail to reject the null hypothesis.
- ○ Not enough information is given.

You may need to use the appropriate table in the [Appendix of Tables](#) to answer this question.
Transcribed Image Text:**Determine the correct critical value of the t-distribution for α = 0.05. (Assume a one-sided test.)** - ○ 1.341 - ○ 1.753 - ○ 2.345 - ○ 2.947 - ○ 3.733 **Should you reject or fail to reject the null hypothesis, or is there not enough information to decide? A sample statistic is tested with α = 0.05, and the corresponding t-value is 1.8 for this sample.** - ○ Reject the null hypothesis. - ○ Fail to reject the null hypothesis. - ○ Not enough information is given. You may need to use the appropriate table in the [Appendix of Tables](#) to answer this question.
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