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 choicesThe 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 populationIt is a case which need Z table to find value of confidence intervalalternative hypothesis statement should be written as greater thanalternative hypothesis statement should be written as greater thanThis is a case of two tail problem
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 choicesThe 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 populationIt is a case which need Z table to find value of confidence intervalalternative hypothesis statement should be written as greater thanalternative hypothesis statement should be written as greater thanThis is a case of two tail problem
Solution
To answer this question, we first need to calculate the sample mean and standard deviation.
The sample mean (x̄) is the sum of all the values divided by the number of values.
The sample standard deviation (s) is the square root of the variance, which is the average of the squared differences from the mean.
Next, we need to set up our null and alternative hypotheses. The null hypothesis (H0) is that the population mean (μ) is equal to 9.8. The alternative hypothesis (H1) depends on the question. If we're testing whether the population mean is not equal to 9.8, then H1: μ ≠ 9.8. If we're testing whether the population mean is greater than 9.8, then H1: μ > 9.8. If we're testing whether the population mean is less than 9.8, then H1: μ < 9.8.
Then, we need to choose the appropriate statistical test. Since we're dealing with a small sample size (n < 30) and we don't know the population standard deviation, we should use a t-test. If we were dealing with a large sample size (n ≥ 30) or we knew the population standard deviation, we would use a z-test.
Finally, we need to determine whether this is a one-tailed or two-tailed test. If the alternative hypothesis is that the population mean is not equal to 9.8 (H1: μ ≠ 9.8), then this is a two-tailed test. If the alternative hypothesis is that the population mean is greater than or less than 9.8 (H1: μ > 9.8 or H1: μ < 9.8), then this is a one-tailed test.
So, the answer choices that apply to this case are:
- 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 single tail problem if the mean of the sample is larger than the mean of the population and we're testing whether the population mean is greater than 9.8
- The alternative hypothesis statement should be written as greater than if we're testing whether the population mean is greater than 9.8
- This is a case of a two-tail problem if we're testing whether the population mean is not equal to 9.8.
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