Pulmonary Disease A study was performed looking at the effect of mean ozone exposure on change in pulmonary function. Fifty hikers were recruited into the study; 25 study participants hiked on days with low-ozone exposure, and 25 hiked on days with high-ozone exposure. The change in pulmonary function after a 4-hour hike was recorde participant. The results are given in the table below. (Let population 1 be high-ozone exposure and population 2 be low-ozone exposure. Use high-low.) Comparison of change in FEV on high-ozone vs. low-ozone days Ozone level Mean change in FEV* 0.102 High Low I USE SALT 0.049 sd 0.254 25 0.105 25 (a) What test can be used to determine whether the mean change in FEV differs between the high-ozone and low-ozone days? (You may need to use the Distribution Calculators page in SALT to check conditions.) O paired t test OF test for the equality of two variances O two-sample t test for independent samples with equal variances O two-sample t test for independent samples with unequal variances (b) Implement the test in part (a), and report a p-value (two-tailed). (Use a 0.05.) State the null and alternative hypotheses (in L). (Enter - for as needed.) Ho: Find the test statistic. (Round your answer to two decimal places.) Use technology to find the p-value. (Round your answer to four decimal places.) p-value= State your conclusion. Fail to reject Ho. There is insufficient evidence to conclude that the mean change in FEV differs between the high-ozone and low-ozone days. O Reject Ho. There is insufficient evidence to conclude that the mean change in FEV differs between the high-ozone and low-ozone days. O Fail to reject Ho. There is sufficient evidence to conclude that the mean change in FEV differs between the high-ozone and low-ozone days. O Reject Ho. There is sufficient evidence to conclude that the mean change in FEV differs between the high-ozone and low-ozone days. (c) Suppose we determine a 95% CI for the true mean change in pulmonary function on high-ozone days. Is this CI narrower, wider, or the same width as a 90% CI? (Do not actually compute the CI.) O The 95% CI is narrower than the 90% CI. O The 95% CI is wider than the 90% CI.
Pulmonary Disease A study was performed looking at the effect of mean ozone exposure on change in pulmonary function. Fifty hikers were recruited into the study; 25 study participants hiked on days with low-ozone exposure, and 25 hiked on days with high-ozone exposure. The change in pulmonary function after a 4-hour hike was recorde participant. The results are given in the table below. (Let population 1 be high-ozone exposure and population 2 be low-ozone exposure. Use high-low.) Comparison of change in FEV on high-ozone vs. low-ozone days Ozone level Mean change in FEV* 0.102 High Low I USE SALT 0.049 sd 0.254 25 0.105 25 (a) What test can be used to determine whether the mean change in FEV differs between the high-ozone and low-ozone days? (You may need to use the Distribution Calculators page in SALT to check conditions.) O paired t test OF test for the equality of two variances O two-sample t test for independent samples with equal variances O two-sample t test for independent samples with unequal variances (b) Implement the test in part (a), and report a p-value (two-tailed). (Use a 0.05.) State the null and alternative hypotheses (in L). (Enter - for as needed.) Ho: Find the test statistic. (Round your answer to two decimal places.) Use technology to find the p-value. (Round your answer to four decimal places.) p-value= State your conclusion. Fail to reject Ho. There is insufficient evidence to conclude that the mean change in FEV differs between the high-ozone and low-ozone days. O Reject Ho. There is insufficient evidence to conclude that the mean change in FEV differs between the high-ozone and low-ozone days. O Fail to reject Ho. There is sufficient evidence to conclude that the mean change in FEV differs between the high-ozone and low-ozone days. O Reject Ho. There is sufficient evidence to conclude that the mean change in FEV differs between the high-ozone and low-ozone days. (c) Suppose we determine a 95% CI for the true mean change in pulmonary function on high-ozone days. Is this CI narrower, wider, or the same width as a 90% CI? (Do not actually compute the CI.) O The 95% CI is narrower than the 90% CI. O The 95% CI is wider than the 90% CI.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Pulmonary Disease
A study was performed looking at the effect of mean ozone exposure on change in pulmonary function. Fifty hikers were recruited into the study; 25 study participants hiked on days with low-ozone exposure, and 25 hiked on days with high-ozone exposure. The change in pulmonary function after a 4-hour hike was recorded for each
participant. The results are given in the table below. (Let population 1 be high-ozone exposure and population 2 be low-ozone exposure. Use high-low.)
Comparison of change in FEV on high-ozone vs.
low-ozone days
Ozone level Mean change in FEV*
High
H₁:
Low
USE SALT
0.102
0.049
sd
0.254 25
0.105 25
(a) What test can be used to determine whether the mean change in FEV differs between the high-ozone and low-ozone days? (You may need to use the Distribution Calculators page in SALT to check conditions.)
O paired t test
O F test for the equality of two variances
O two-sample t test for independent samples with equal variances
O two-sample t test for independent samples with unequal variances
(b) Implement the test in part (a), and report a p-value (two-tailed). (Use a = 0.05.)
State the null and alternative hypotheses (in L). (Enter != for as needed.)
Ho:
Find the test statistic. (Round your answer to two decimal places.)
Use technology to find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
O Fail to reject Ho. There is insufficient evidence to conclude that the mean change in FEV differs between the high-ozone and low-ozone days.
O Reject Ho. There is insufficient evidence to conclude that the mean change in FEV differs between the high-ozone and low-ozone days.
O Fail to reject Ho. There is sufficient evidence to conclude that the mean change in FEV differs between the high-ozone and low-ozone days.
O Reject Ho. There is sufficient evidence to conclude that the mean change in FEV differs between the high-ozone and low-ozone days.
(c) Suppose we determine a 95% CI for the true mean change in pulmonary function on high-ozone days. Is this CI narrower, wider, or the same width as a 90% CI? (Do not actually compute the CI.)
O The 95% CI is narrower than the 90% CI.
O The 95% CI is wider than the 90% CI.
O The 95% CI is the same width as the 90% CI.
Expert Solution
Step 1
The t-distribution is very useful probability distribution when the sample size is small and the population variance is unknown. It is also used for population with unknown variance. It is used as an alternative to normal distribution in the cases mentioned.
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