Question

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.

Answer #1

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

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