A researcher takes sample temperatures in Fahrenheit of 17 days from San Diego and 15 days from Las Vegas. Use the sample data shown in the table below.

San Diego: 112.5, 76.7, 63.9, 73.6, 89.3, 70.5, 70, 73.2, 65, 56.4, 117.7, 85.3, 83.6, 71, 103.1, 74, 70.8

Las Vegas: 99.1, 57.7, 80.3, 92.8, 54.1, 73.2, 71.4, 105.7, 84.7, 74.6, 84.2, 75.9, 55.7, 68.2, 101.3

Test the claim that the mean temperature in San Diego is different from the mean temperature in Las Vegas. Use a significance level of \(\alpha\). Assume the populations are approximately normally distributed with unequal variances.

Note: List 1 is longer than list 2, so these are 2 independent samples, not matched pairs.

The null hypothesis is: \(H_0: \mu_1 - \mu_2 = 0\)

What is the alternative hypothesis? Select the correct symbols for each space.

Question

26-09-2024
Mathematics

High School

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A researcher takes sample temperatures in Fahrenheit of 17 days from San Diego and 15 days from Las Vegas. Use the sample data shown in the table below.

San Diego: 112.5, 76.7, 63.9, 73.6, 89.3, 70.5, 70, 73.2, 65, 56.4, 117.7, 85.3, 83.6, 71, 103.1, 74, 70.8

Las Vegas: 99.1, 57.7, 80.3, 92.8, 54.1, 73.2, 71.4, 105.7, 84.7, 74.6, 84.2, 75.9, 55.7, 68.2, 101.3

Test the claim that the mean temperature in San Diego is different from the mean temperature in Las Vegas. Use a significance level of \(\alpha\). Assume the populations are approximately normally distributed with unequal variances.

Note: List 1 is longer than list 2, so these are 2 independent samples, not matched pairs.

The null hypothesis is: \(H_0: \mu_1 - \mu_2 = 0\)

What is the alternative hypothesis? Select the correct symbols for each space.

Answer :

Final answer:

The alternative hypothesis is Ha: μ1 - μ2 ≠ 0, indicating that the mean temperature in San Diego is different from the mean temperature in Las Vegas.

Explanation:

The alternative hypothesis for the given problem can be stated as Ha: μ1 - μ2 ≠ 0. This means that the mean temperature in San Diego is different from the mean temperature in Las Vegas.

In hypothesis testing, the null hypothesis (H0) assumes that there is no significant difference between the two means, while the alternative hypothesis (Ha) states that there is a significant difference. The symbols ≠ in the alternative hypothesis indicate that we are testing for a two-tailed alternative.

To test the claim, a t-test can be performed using the given sample data, assuming unequal variances and a significance level of α = 0.05 (5%). The calculated t-value can be compared to the critical t-value at the desired significance level to determine if the null hypothesis should be rejected or not.

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