Reference no: EM132178438

1. In a study on air quality, it is suggested that pollution levels have changed over the last decade. In particular, the researchers argue that carbon monoxide pollution is no longer at the 1990 level of 11ppm.To test their hypothesis, they take a sample of 120 carbon monoxide (CO) measurements. The average CO levels in the sample are x= 10.7ppm and the estimated standard deviation is s= 1.9ppm. Assume a significance level of 0.05.

a. Is this a one sided or a two sided test?

b. What are the null and alternative hypotheses that the researchers should test?

c. What will be the distribution of the statistic that you will use to test these hypotheses? (z or t)

d. Calculate the statistic.

e. What is the critical value from the corresponding distribution tables for this particular case? How did you choose these value (explicitly state whether you are looking at the statistic for α or α/ 2 and if necessary, what are the degrees of freedom).

f. Would you reject the Null Hypothesis? Why?

2. Say a researcher is interested in knowing whether differences in recreation behavior exist between the central city (CC) and suburban regions (SR) of a metropolitan area. In particular, the researcher is interested in swimming frequencies. There is no a prior knowledge so the researcher just wants to test whether the mean annual swimming frequencies from the city center are different from those from the suburban regions. For a sample size of only 8 individuals from each part of the city, we have that the mean for the CC is 48.63. For the SR the sample mean is 63. Assume the variance is the same for both samples so that the standard deviation for each sample is 12.66. For a significance level of 5% test the hypothesis in which the researcher is interested.

a. What are the null and alternative hypotheses?

b. Since the sample is really small (only 8 for each section of the city) you should use a t statistic. Calculate the t statistic for the researcher's question.

c. Would you reject the null hypothesis of the researcher for a 5% significance level?

d. Now assume that the standard deviations for the two samples are different. For the CC the standard deviation for the sample is 19.88 and the sample standard deviation for the SR is 12.66. Calculate your new test statistic. Does your final conclusion change; would you reject the null hypothesis?

e. Would your final conclusion change in any of the two cases (equal vs. different variances for the two samples) if you choose instead a 10% significance level? How does it change and why?