Consider the following hypothesis test. Ho: µ 1 - µ 2 = 0 Ha: µ 1 - µ 2 0 The following results are from independent samples taken from two populations. Sample 1 Sample 2 ni = 35 n 2 = 40 | X 1 = 13.6 X 2 = 10.1 S 1 = 5.3 S 2 = 8.6 a. What is the value of the test statistic (to 2 decimals)? b. What is the degrees of freedom for the t distribution? (Round down your answer to the whole number) c. What is the p-value? Use z-table. The area in the upper tail is Select ; two-tailed p-value is between select d. At a = .05, what is your conclusion? p-value is Select Но

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**Hypothesis Test Example**

Consider the following hypothesis test:

- \( H_0: \mu_1 - \mu_2 = 0 \)
- \( H_a: \mu_1 - \mu_2 \neq 0 \)

The following results are from independent samples taken from two populations:

**Sample 1:**
- \( n_1 = 35 \)
- \( \bar{X}_1 = 13.6 \)
- \( s_1 = 5.3 \)

**Sample 2:**
- \( n_2 = 40 \)
- \( \bar{X}_2 = 10.1 \)
- \( s_2 = 8.6 \)

**Questions:**

a. What is the value of the test statistic (to 2 decimals)?

\[ \text{Answer box} \]

b. What is the degrees of freedom for the \( t \) distribution? (Round down your answer to the whole number)

\[ \text{Answer box} \]

c. What is the \( p \)-value? Use the [z-table](#).

- The area in the upper tail is \(\text{Select}\).
- Two-tailed \( p \)-value is between \(\text{Select}\).

d. At \( \alpha = .05 \), what is your conclusion?

- \( p \)-value is \(\text{Select}\) \( H_0 \)
Transcribed Image Text:**Hypothesis Test Example** Consider the following hypothesis test: - \( H_0: \mu_1 - \mu_2 = 0 \) - \( H_a: \mu_1 - \mu_2 \neq 0 \) The following results are from independent samples taken from two populations: **Sample 1:** - \( n_1 = 35 \) - \( \bar{X}_1 = 13.6 \) - \( s_1 = 5.3 \) **Sample 2:** - \( n_2 = 40 \) - \( \bar{X}_2 = 10.1 \) - \( s_2 = 8.6 \) **Questions:** a. What is the value of the test statistic (to 2 decimals)? \[ \text{Answer box} \] b. What is the degrees of freedom for the \( t \) distribution? (Round down your answer to the whole number) \[ \text{Answer box} \] c. What is the \( p \)-value? Use the [z-table](#). - The area in the upper tail is \(\text{Select}\). - Two-tailed \( p \)-value is between \(\text{Select}\). d. At \( \alpha = .05 \), what is your conclusion? - \( p \)-value is \(\text{Select}\) \( H_0 \)
**Text Transcription for Educational Website:**

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The U.S. Department of Transportation provides the number of miles that residents of the 75 largest metropolitan areas travel per day in a car. Suppose that for a simple random sample of 70 Buffalo residents the mean is 22.6 miles a day and the standard deviation is 8.5 miles a day, and for an independent simple random sample of 40 Boston residents the mean is 18.6 miles a day and the standard deviation is 7.8 miles a day.

Round your answers to one decimal place.  

**a.** What is the point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day?

\[ \_\_\_\_ \]

**b.** What is the 95% confidence interval for the difference between the two population means? Use z-table.

\[ \_\_\_\_ \] to \[ \_\_\_\_ \]

---
Transcribed Image Text:**Text Transcription for Educational Website:** --- The U.S. Department of Transportation provides the number of miles that residents of the 75 largest metropolitan areas travel per day in a car. Suppose that for a simple random sample of 70 Buffalo residents the mean is 22.6 miles a day and the standard deviation is 8.5 miles a day, and for an independent simple random sample of 40 Boston residents the mean is 18.6 miles a day and the standard deviation is 7.8 miles a day. Round your answers to one decimal place. **a.** What is the point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day? \[ \_\_\_\_ \] **b.** What is the 95% confidence interval for the difference between the two population means? Use z-table. \[ \_\_\_\_ \] to \[ \_\_\_\_ \] ---
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