Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.8 parts/ million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 9 samples is 4.3 PPM with a standard deviation of 0.6. Assume the population is normally distributed. A level of significance of 0.05 will be used. find the value of the test to statistic. round your answer to 3 decimal places.

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Asked Apr 12, 2019
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Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.8 parts/ million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 9 samples is 4.3 PPM with a standard deviation of 0.6. Assume the population is normally distributed. A level of significance of 0.05 will be used. find the value of the test to statistic. round your answer to 3 decimal places.

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Expert Answer

Step 1

Here, the sample size is 9 that is reasonably small. The population standard deviation is unknown here. Therefore, z-test cannot be used here. In this situation student’s t-distribution can be used.

Let µ be the true mean level of ozone.

Let x bar be the sample mean level of ozone. s be the sample standard deviation. n is the sample size.

Step 2

State the appropriate null and alternative hypotheses:

Null hypothesis:

H0 : μ = 4.8

Alternative hypothesis:

H1 : μ ≠ 4.8

Test statistic:

The test statistic for t test is given by:

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Step 3

Here, n = 9and μ0 = 4.8. The mean and standard deviation for the data is 4.3 and 0.6 res...

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Statistics

Hypothesis Testing

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