Question

A simple random sample of 33 men from a normally distributed population results in a standard deviation of 8.2 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal​ range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts​ (a) through​ (d) below.

a. Identify the null and alternative hypotheses.

b. Compute the test statistic; χ2 = ___ ​(Round to three decimal places as​ needed.)

c. Find the​ P-value; ​P-value = ____ ​(Round to four decimal places as​ needed.)

d. State the conclusion. (choose one from each ( x, y) set)

Answer 1

Data Summary      
       
s = 8.2 beats per minute  Sample standard deviation    
n = 33  Sample size of men    
σ = 10 beats per minute  Population or standardized standard deviation    
α = 0.10  Level of significance    
       
       
a) To test the given hypothesis, we will use a   two-tailed test.       
Since we want to test if the standard deviation is equal(or not equal) to 10 beats per minute      
Hence the null and alternative hypothesis are       
Ho : σ = 10      
HA : σ ≠ 10      
       
b) χ2 test statistic is calculated as given below       

χ2 = 21.517      
       
c) df = degrees of freedom = n - 1 = 33 - 1 = 32      
we find the p-value using Excel function CHISQ.DIST.RT(chisquare statistic, df)      
Since it is a two sided test we do 2*(1 - CHISQ.DIST.RT(chisquare statistic, df))      
p-value = 2*(1 - CHISQ.DIST.RT(21.517, 32))      
                = 0.1606      
P-value = 0.1606      
       
d) 0.1606 > 0.10      
that is p-value > α      
Hence, we DO NOT reject Ho      
Conclusion :      
Pulse rates of men have a standard deviation equal to 10 beats per minute      
       
Note to student : You have not provided the (x,y) set      
Hence choose the correct option according to the conclusion provided above