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 () is to be performed. What pieces of information are needed in order to calculate the corresponding z test statistic?

1- the level of significance used

2- the proposed population mean

3- the characteristic of interest

4- the actual population mean

5- the sample mean calculated

6-the population standard deviation

7-the size of the sample selected

Consider the hypothesis test with the following null and alternative hypotheses:

H₀:= 0.5

H_A:> 0.5

If the level of significance used is = 0.05, the region of rejection is the set of numbers:

a) whose absolute value is less than 1.645

b) greater than 1.96

c) whose absolute value is greater than 1.645

d) greater than 1.645

e) whose absolute value is greater than 1.96

f) less than -1.96

g) whose absolute value is less than 1.96

h) less than -1.645

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 31 minutes and the standard deviation is 5 minutes.

The manufacturers would like to construct a hypothesis test for the mean time () taken for Painadene tablets to relieve pain assuming the same population standard deviation () 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 29.54 minutes. The hypotheses that will be used by the manufacturers areH₀: = 31andH_A: 31.

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 = 0.05, Painadol should:

1.accept the null hypothesis

2.reject the null hypothesis

3.not reject the null hypothesis