Question

A medical researcher wants to compare the pulse rates of smokers and non-smokers. He believes that the pulse rate for smokers and non-smokers is different and wants to test this claim at the 0.02 level of significance. A sample of 46 smokers has a mean pulse rate of 75, and a sample of 47 non-smokers has a mean pulse rate of 73. The population standard deviation of the pulse rates is known to be 7 for smokers and 10 for non-smokers. Let μ1 be the true mean pulse rate for smokers and μ2 be the true mean pulse rate for non-smokers. Step 1 of 4: State the null and alternative hypotheses for the test. Step 2 of 4: Compute the value of the test statistic. Round your answer to two decimal places. Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to two decimal places. Step 4 of 4: Make the decision for the hypothesis test.

Answer 1

: the true mean pulse rate for smokers

: the true mean pulse rate for non-smokers

Sample 1 - Smokers : A sample of 46 smokers has a mean pulse rate of 75

Sample 2- Non Smokers : A sample of 47 non-smokers has a mean pulse rate of 73

The population standard deviation of the pulse rates for smokers : = 7

The population standard deviation of the pulse rates for nonsmokers : = 10

Level of Significance : = 0.02

Step1 of 4 :

Null and alternative hypotheses for the test

Null hypothesis H_o:

Alternate Hypothesis : H_a : Two Tailed Test

Step 2 of 4: Compute the value of the test statistic:

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H_o

For Two tailed test; Reject null hypothesis if Calculated Value of Z_stat < Z_/2 or Z_stat > Z_1-/2

p-value approach:

If P-Value is less than Level of significance: then Reject Null Hypothesis

Step 4 of 4

= 0.02; /2 = 0.02/2 = 0.01

As Calculated Value is with in the Critical Values i.e.( -2.33 < 1.1193 < 2.33 )Fail To Reject Null Hypothesis

p-value

As P-Value i.e. is greater than Level of significance i.e (P-value:0.263 > 0.02:Level of significance); Fail to Reject Null Hypothesis

Using Excel Function to find the P-value : NORM.S.DIST function

NORM.S.DIST function
Returns the standard normal distribution (has a mean of zero and a standard deviation of one).
Use this function in place of a table of standard normal curve areas.Syntax – Standard Normal DistributionNORM.S.DIST(z,cumulative)
The NORM.S.DIST function syntax has the following arguments:
## Z Required. The value for which you want the distribution.
## Cumulative Required. Cumulative is a logical value that determines the form of the function. If cumulative is TRUE, NORMS.DIST returns the cumulative distribution function; if FALSE, it returns the probability mass function.