A researcher is studying how much electricity (in kilowatt hours) people from two different cities use in their homes. Random samples of 15 days from Kansas City (Group 1) and 15 days from Miami (Group 2) are shown below. Test the claim that the mean number of kilowatt hours in Kansas City greater than the mean number of kilowatt hours in Miami. Use a significance level of a = 0.01. Assume the populations are approximately normally distributed with unequal variances. Round answers to 4 decimal places. Kansas City Miami 837.6 836.5 841.5 844.4 845.2 839.5 844.3 830.9 842.5 837.4 839 843.1 852.5 832.5 850.4 841.6 830.7 848.2 837.8 833.3 853.1 844.7 837.6 839.2 842.5 838.9 837.2 835.5 835.6 845.1 What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols for each of the 6 spaces. Hoi LH, H₁: ₁ Based on the hypotheses, find the following: Test Statistic = p-value = of H₂ The p-value is greater than alpha OF H₂ oto alpha. The correct decision is to fail to reject the null hypothesis The correct summary would be: There is not enough evidence to support ✓ the claim that the mean

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A researcher is studying how much electricity (in kilowatt hours) people from two different cities use in their homes. Random samples of 15 days from Kansas City (Group 1) and 15 days from Miami (Group 2) are shown below. Test the claim that the mean number of kilowatt hours in Kansas City greater than the mean number of kilowatt hours in Miami. Use a significance level of \(\alpha = 0.01\). Assume the populations are approximately normally distributed with unequal variances. Round answers to 4 decimal places.

| Kansas City | Miami  |
|-------------|--------|
| 837.6       | 836.5  |
| 841.5       | 844.4  |
| 845.2       | 839.5  |
| 844.3       | 830.9  |
| 842.5       | 837.4  |
| 839         | 843.1  |
| 852.5       | 832.5  |
| 850.4       | 841.6  |
| 830.7       | 848.2  |
| 837.8       | 833.3  |
| 853.1       | 844.7  |
| 837.6       | 839.2  |
| 842.5       | 838.9  |
| 837.2       | 835.5  |
| 835.6       | 845.1  |

### What are the correct hypotheses?

* \( H_0: \mu_1 = \mu_2 \)
* \( H_1: \mu_1 > \mu_2 \)

### Based on the hypotheses, find the following:

- **Test Statistic =** 
- **p-value =** 
- *The p-value is greater than alpha.*

### The correct decision is to:

- **Fail to reject the null hypothesis.**

### The correct summary would be:

- **There is not enough evidence to support** the claim that the mean number of kilowatt hours in Kansas City is greater than that in Miami.
Transcribed Image Text:A researcher is studying how much electricity (in kilowatt hours) people from two different cities use in their homes. Random samples of 15 days from Kansas City (Group 1) and 15 days from Miami (Group 2) are shown below. Test the claim that the mean number of kilowatt hours in Kansas City greater than the mean number of kilowatt hours in Miami. Use a significance level of \(\alpha = 0.01\). Assume the populations are approximately normally distributed with unequal variances. Round answers to 4 decimal places. | Kansas City | Miami | |-------------|--------| | 837.6 | 836.5 | | 841.5 | 844.4 | | 845.2 | 839.5 | | 844.3 | 830.9 | | 842.5 | 837.4 | | 839 | 843.1 | | 852.5 | 832.5 | | 850.4 | 841.6 | | 830.7 | 848.2 | | 837.8 | 833.3 | | 853.1 | 844.7 | | 837.6 | 839.2 | | 842.5 | 838.9 | | 837.2 | 835.5 | | 835.6 | 845.1 | ### What are the correct hypotheses? * \( H_0: \mu_1 = \mu_2 \) * \( H_1: \mu_1 > \mu_2 \) ### Based on the hypotheses, find the following: - **Test Statistic =** - **p-value =** - *The p-value is greater than alpha.* ### The correct decision is to: - **Fail to reject the null hypothesis.** ### The correct summary would be: - **There is not enough evidence to support** the claim that the mean number of kilowatt hours in Kansas City is greater than that in Miami.
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