A particular characteristic is of interest to a researcher. The researcher is particularly interested in the mean
Question
A particular characteristic is of interest to a researcher. The researcher is particularly interested in the mean
value of this characteristic in the population. A hypothesis test for the mean (μ) is to be performed. Select all the pieces of information that are needed in order to calculate the corresponding z test statistic:
| the actual population mean |
| the proposed population mean |
| the characteristic of interest |
| the population standard deviation |
| the sample mean calculated |
| the size of the sample selected |
| the level of significance used |
You may find the standard normal table useful in answering this question. Consider the hypothesis test with the following null and alternative hypotheses:
H0: = 0.7
HA: > 0.7
If the level of significance used is α = 0.05, the region of rejection is the set of numbers:
| greater than 1.645 |
| whose absolute value is greater than 1.645 |
| whose absolute value is greater than 1.96 |
| whose absolute value is less than 1.645 |
| whose absolute value is less than 1.96 |
| less than -1.645 |
| greater than 1.96 |
| less than -1.96 |
Painadol is a well trusted, popular pain-killer used by millions throughout the country. Recently an epidemic of headaches has hit the nation and the manufacturers of Painadol have created a new, stronger painkiller called Painadene. The manufacturers are interested in testing whether the speed of pain relief is different with Painadene. It is known that the mean time taken by Painadol tablets to relieve pain is 29 minutes and the standard deviation is 6 minutes.
The manufacturers would like to construct a hypothesis test for the mean time (μ) taken for Painadene tablets to relieve pain assuming the same population standard deviation (σ) as the Painadol tablets. A random sample of 34 people with headaches tried the new Painadene tablets and the mean time taken to relieve the pain was calculated as 27.21 minutes. The hypotheses that will be used by the manufacturers are H0: μ = 29 and HA: μ ≠ 29.
You may find this standard normal table useful throughout the following questions.
a)Calculate the test statistic (z) that corresponds to the sample and hypotheses. Give your answer as a decimal to 3 decimal places.
z =
b)Using the test statistic for Painadol’s hypothesis test and a level of significance of α = 0.1, Painadol should acceptrejectnot reject the null hypothesis.
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