Question

# 3. The average pulse rate is known to be 80 beats per minutes. Suppose we take...

3. The average pulse rate is known to be 80 beats per minutes. Suppose we take a sample of 30 adults and find that the average heart rate in the sample is 73.76 with a sample standard deviation of 7.06. We are interested in testing if the average pulse rate is actually lower than 80 beats per minute. ( please show all steps and how you got each number)

a. Using the sample of 30 adults, what would the 95% confidence interval be for the population mean?

b. What are the null and alternative hypotheses?

c. What is the critical value at 95% confidence?

d. Calculate the test statistic.

e. Find the p-value. f. What conclusion would be made here at the 95% confidence level?

g. Would my conclusion change if I changed alpha to .01? Show reasoning.

a)

b)

 null hypothesis: μ = 80 Alternate Hypothesis: μ < 80

c)

 for 0.05 level with left tailed test and n-1= 29 degree of freedom, critical value of t= -1.699

d)

tst statsitic =(Xbar-mean)/std error=(73.76-80)/1.289=-4.841

e)

p value =0.0000

f)

Decision:as test statistic is in rejection region we reject null hypothesis

Conclusion: we have sufficient evidence to conclude that average pulse rate is actually lower than 80 beats per minute

g)

our conclusion will remain same as p value is still less then alpha level