CASE STUDYIn air pollution study, Ozon measurement were taken in a large California city at 5.00 PM. The eight readings (in parts per million) were7.9, 11.3, 6.9 , 12.7, 13.2, 8.8, 9.3 , 10.6Assuming the population sampled is normal. Test the null hypothesis for population mean 9.8.choose all possible options for the caseGroup of answer choicesalternative hypothesis statement should be written as greater thanIt is a case which need Z table to find value of confidence intervalThe alternative hypothesis should be stated as less then or greater thanIt is a case which need t table to find value of confidence intervalThis is a case of single tail problem as the mean of sample is larger than the mean of populationThis is a case of two tail problemalternative hypothesis statement should be written as greater than
Question
CASE STUDYIn air pollution study, Ozon measurement were taken in a large California city at 5.00 PM. The eight readings (in parts per million) were7.9, 11.3, 6.9 , 12.7, 13.2, 8.8, 9.3 , 10.6Assuming the population sampled is normal. Test the null hypothesis for population mean 9.8.choose all possible options for the caseGroup of answer choicesalternative hypothesis statement should be written as greater thanIt is a case which need Z table to find value of confidence intervalThe alternative hypothesis should be stated as less then or greater thanIt is a case which need t table to find value of confidence intervalThis is a case of single tail problem as the mean of sample is larger than the mean of populationThis is a case of two tail problemalternative hypothesis statement should be written as greater than
Solution
The null hypothesis (H0) in this case would be that the population mean is equal to 9.8 (H0: μ = 9.8). The alternative hypothesis (H1) could be that the population mean is not equal to 9.8 (H1: μ ≠ 9.8). This would be a two-tailed test because we are considering the possibility that the population mean could be either greater than or less than 9.8.
To test these hypotheses, we would first calculate the sample mean and the sample standard deviation. Then, we would use a t-test because the population standard deviation is unknown and the sample size is small (n < 30). The t-test compares the sample mean to the population mean, taking into account the sample size and variability.
If the calculated t-value falls within the critical region determined by the t-distribution and the chosen significance level (commonly 0.05), we would reject the null hypothesis in favor of the alternative hypothesis. If the calculated t-value does not fall within the critical region, we would not reject the null hypothesis.
So, the correct options would be:
- The alternative hypothesis should be stated as less than or greater than
- It is a case which needs a t-table to find the value of the confidence interval
- This is a case of a two-tail problem.
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