Question

women between the ages of 70 and 80 were randomly selected from the general population of women in this age group to take part in a special program to decrease reaction time​ (speed). After the​ course, the women had an average reaction time of 1.7 seconds. Assume that the mean reaction time for the general population of women in this age group is 1.9​, with a standard deviation of 0.6 seconds.​ (Assume that the population is approximately​ normal.) Use this information to complete parts​ (a) through​ (d). Click here to view page 1 of the table. LOADING... Click here to view page 2 of the table. LOADING... Click here to view page 3 of the table. LOADING... Click here to view page 4 of the table. LOADING... ​(a) Carry out a Z test using the five steps of hypothesis testing​ (use the 0.01​ level). Choose a research hypothesis and a null hypothesis. Choose the correct answer below. A. The research hypothesis is the mean of the populations are the same. The null hypothesis is the mean of the populations are not the same. B. The research hypothesis is the mean of the sample population is less than the mean of the general population. The null hypothesis is the mean of the sample population is greater than or equal to the mean of the general population. This is the correct answer.C. The research hypothesis is the mean of the populations are not the same. The null hypothesis is the mean of the populations are the same. Your answer is not correct.D. The research hypothesis is the mean of the sample population is greater than or equal to the mean of the general population. The null hypothesis is the mean of the sample population is less than or equal to the mean of the general population. Assume that the distribution of means is approximately normal. What​ is/are the cutoff sample​ score(s) on the comparison distribution at which the null hypothesis should be​ rejected? nothing ​(Use a comma to separate answers as needed. Type an integer or decimal rounded to two decimal places as​ needed.)

Answer 1

Given that,
population mean(u)=1.7
standard deviation, sigma =0.6
sample mean, x =1.9
Assume,number (n)=10
null, Ho: μ=1.7
alternate, H1: μ!=1.7
level of significance, alpha = 0.01
from standard normal table, two tailed z alpha/2 =2.576
since our test is two-tailed
reject Ho, if zo < -2.576 OR if zo > 2.576
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 1.9-1.7/(0.6/sqrt(10)
zo = 1.05
| zo | = 1.05
critical value
the value of |z alpha| at los 1% is 2.576
we got |zo| =1.05 & | z alpha | = 2.576
make decision
hence value of |zo | < | z alpha | and here we do not reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 1.05 ) = 0.29
hence value of p0.01 < 0.29, here we do not reject Ho
ANSWERS
---------------
a.
null, Ho: μ=1.7
alternate, H1: μ!=1.7
option:C.
The research hypothesis is the mean of the populations are not the same.
The null hypothesis is the mean of the populations are the same
test statistic: 1.05
critical value: -2.576 , 2.576
decision: do not reject Ho
p-value: 0.29
we do not have enough evidence to support the claim