Question

Forty refrigerators from two different models of a refrigerator manufacturer are compared to see if the smaller model uses less energy than the larger model. The energy was measured in kilowatt hours per month (kwh/mo). From years of testing these models, it is known that the standard deviation of kwh/mo is 34 kwh/mo for the smaller model and 40 kwh/mo for the larger one. From this survey, the sample means and standard deviations are 125 and 34, and 90 and 40, respectively. If we conduct a hypothesis test, the p-value is O 0.0000 O 0.0002 O 0.0004 O 0.0010 Question 4 1 pts A study is done to determine if baby girls start walking, on average, before baby boys. Fourteen girls and fourteen boys are surveyed. The average ages were 11.4 months for girls with a standard deviation of 0.6 months, and 13.2 months for boys with a standard deviation of 0.7 months. The hypothesis test to use is O two proportions independent group means, population standard deviations unknown O matched or paired samples independent group means, population standard deviations known

Answer 1

3.

The provided sample means are shown below: X1 = 125 X = 90 Also, the provided population standard deviations are: 01 = 40 02 = 34 and the sample sizes are ni 40 and n2 = 40.

Ho: Mi = 42 Ηα: μι 2 μ2 This corresponds to a right-tailed test, for which a z-test for two population means, with known population standard deviations will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a right-tailed test is ze = 1.64. The rejection region for this right-tailed test is R = {z:z> 1.64} (3) Test Statistics The z-statistic is computed as follows: X1 - X2 Vo/nı + ož/n2 125 - 90 402 /40+ 342 / 40 4.217 (4) Decision about the null hypothesis Since it is observed that z = 4.217 > 2c = 1.64, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p= 0, and since p=0 <0.05, it is concluded that the null hypothesis is rejected.

Hence, p-value = 0

4.

independent group means, population standard deviations unknown

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