Question

Researchers wanted to know if the levels of algae in a pond were hazardous to the fish that lived there. If the average levels are above 30 parts per million (ppm) the pond would be considered hazardous to the health of the fish. In the study with a 5% significance level, researchers collected data and found that the sample mean from 60 samples was 30.829. If σ = 34 , H 0:   m u = 30 ; H a: μ < 30 calculate the test statistic. Assume all assumptions are met.

Group of answer choices

t = 0.1891

t = 6.8347

z = 6.8347

z = 0.1889

t = 0

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Question 96.67 pts

Researchers randomly assign members of a study to one of two groups. The researchers found that for the 99 participants in Group A, the mean was 42.2 minutes and the standard deviation was 16.2 minutes. For Group B, the mean for the 99 participants was 47.9 minutes and the standard deviation was 17.9 minutes. Researchers used the hypotheses ofH 0: μ A − μ B = 30H a: μ A − μ B ≠ 30 . Find the value of the test statistic and the p-value for this study.

Group of answer choices

t = -2.35, p-value = 0.02

z = -2.35, p-value = 0.79

t = 2.35, p-value = 0.02

t = 2.35, p-value = 0.79

t = -2.35, p-value = 0.79

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Question 106.67 pts

Researchers randomly assign members of a study to one of two groups. The researchers found that for the 99 participants in Group A, the means was 42.2 minutes and the standard deviation was 16.2 minutes. For Group B, the mean for the 99 participants was 47.9 minutes and the standard deviation was 17.9 minutes. Researchers used the hypotheses ofH 0: μ A − μ B = 30H a: μ A − μ B ≠ 30 Determine what the conclusion would be for this study if the p-value was (a) 0.02 or (b) 0.79.

Group of answer choices

For a p-value of 0.02, we would not reject the null hypothesis that there is no difference in the mean. For a p-value of 0.79, we would not reject the null hypothesis that there is a difference in the mean.

For a p-value of 0.02, we would reject the null hypothesis that there is no difference in the mean. For a p-value of 0.79, we would not reject the null hypothesis that there is a difference in the mean.

For a p-value of 0.02, we would not reject the null hypothesis that there is no difference in the mean. For a p-value of 0.79, we would reject the null hypothesis that there is no difference in the mean.

For a p-value of 0.02, we would reject the null hypothesis that there is no difference in the mean. For a p-value of 0.79, we would not reject the null hypothesis that there is no difference in the mean.

For a p-value of 0.02, we would not reject the null hypothesis that there is a difference in the mean. For a p-value of 0.79, we would reject the null hypothesis that there is a difference in the mean.

Answer 1

Here we have to test that

where

Sample size = n = 60

Sample mean =

Population standard deviation = = 34

Here Population standard deviation is known so we use z test.

Test statistic:

z = 0.1889 (Round to 4 decimal)

Test statistic = z = 0.1889