5. The resting pulse rates for the entire population has a normal distribution w

Question

5. The resting pulse rates for the entire population has a normal distribution with mean 81. A researcher would like to know whether or not the mean of the population of joggers is less than this. A random sample of 16 joggers gave a mean of 75 and a standard deviation of 12, a=0.05 a. If we do a hypothesis test, which one, a two-sided or one-sided hypothesis, is appropriate? b. What is the null hypothesis and alternative hypothesis? c. What is the value of the test-statistic? d. What is the p-value? e. What conclusion do you reach concerning the mean pulse rate of the population of joggers from which the sample was selected? Use the 5% level of significance. (use on sentence)

Explanation / Answer

5.

Given that,
population mean(u)=81
standard deviation, =12
sample mean, x =75
number (n)=16
null, Ho: =81
alternate, H1: !=81
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 75-81/(12/sqrt(16)
zo = -2
| zo | = 2
critical value
the value of |z | at los 5% is 1.96
we got |zo| =2 & | z | = 1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != -2 ) = 0.046
hence value of p0.05 > 0.046, here we reject Ho
ANSWERS
---------------
a. hypothesis is two sided
b.
null, Ho: =81
alternate, H1: !=81
c.
test statistic: -2
critical value: -1.96 , 1.96
d.
p-value: 0.046
e.
decision: reject Ho
we conclude that the mean pulse rate of population of joggers from which the sample was selected.

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