A recent national survey found that high school students watched an average (mea
ID: 2921305 • Letter: A
Question
A recent national survey found that high school students watched an average (mean) of 7.5 DVDs per month with a population standard deviation of 0.90 hour. The distribution of DVDs watched per month follows the normal distribution. A random sample of 38 college students revealed that the mean number of DVDs watched last month was 7.00. At the 0.05 significance level, can we conclude that college students watch fewer DVDs a month than high school students?
State the null hypothesis and the alternate hypothesis.
State the decision rule.
Compute the value of the test statistic
What is your decision regarding H0?
what is p value?
a.State the null hypothesis and the alternate hypothesis.
State the decision rule.
Compute the value of the test statistic
What is your decision regarding H0?
what is p value?
Explanation / Answer
Given that,
population mean(u)=7.5
standard deviation, =0.9
sample mean, x =7
number (n)=38
null, Ho: >7.5
alternate, H1: <7.5
level of significance, = 0.01
from standard normal table,left tailed z /2 =2.326
since our test is left-tailed
reject Ho, if zo < -2.326
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 7-7.5/(0.9/sqrt(38)
zo = -3.42467
| zo | = 3.42467
critical value
the value of |z | at los 1% is 2.326
we got |zo| =3.42467 & | z | = 2.326
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : left tail - ha : ( p < -3.42467 ) = 0.00031
hence value of p0.01 > 0.00031, here we reject Ho
ANSWERS
---------------
null, Ho: =7.5
alternate,we conclude that college students watch fewer DVDs a
month than high school students H1: <7.5
test statistic: -3.42467
critical value: -2.326
decision: reject Ho
p-value: 0.00031
we have enough evidence to support that college students watch fewer DVDs a
month than high school students