Hypothesis test for single mean.
A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has the normal distribution with an average of 7.4 minutes and a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normal with the same standard deviation, but the mean effective time might be lower. If it is lower, the drug company will market the new anesthetic, otherwise, they would continue to produce the older one. A hypothesis test will be carried out to help make the decision.
1. The appropriate hypotheses are:
a) H_{0}: m = 7.4 versus H_{1}: = m ≠ 7.4
b) H_{0}: m ≤ 7.4 versus H_{1}: = m > 7.4
c) H_{0}: m ≥7.4 versus H_{1}: = m< 7.4
d) H_{0}: m > 7.4 versus H_{1}: = m ≤ 7.4
2. For a test with a level of significance of 0.08, critical value would be _________
3. A sample of size 36 results in a sample mean of 7.1. The value of the test statistic is ____
4. A sample of size 36 results in a sample mean of 7.1. The p-value of the test is _____
5. A sample of size 36 results in a sample mean of 7.1. The null hypothesis will be rejected with a level of significance of 0.05. True or False?
6. A sample of size 36 results in a sample mean of 7.1. If the level of importance had been chosen as 0.01, the company would market the new anesthetic. True or False?
7. Which of the following can be an appropriate null hypothesis?
a) The population proportion is less than 0.65
b) the sample proportion is less than 0.65.
c) The population proportion is less than or equal to 0.65
d) the sample proportion is less than or equal to 0.65 C