In a recent survey of 150 Americans, researchers concluded that those surveyed w
ID: 3313449 • Letter: I
Question
In a recent survey of 150 Americans, researchers concluded that those surveyed watch television on average 4 hours per day with a standard deviation of 2 hours per day. Conduct a hypothesis test to determine if there is any validity to the claim that Americans watch less than 3.2 hours of television per day. Test this claim at the .05 level of significance.
1. Identify the claim, and write the claim, the null hypothesis, and the alternative hypothesis in symbolic form.
2. Determine if the test is two-tailed, right-tailed, or left-tailed, and determine the value of the test statistic.
3. Find the P-value, and use it to either reject or fail to reject the null hypothesis.
4. Write your conclusion in a complete sentence in plain English.
Explanation / Answer
Given that,
population mean(u)=3.2
sample mean, x =4
standard deviation, s =2
number (n)=150
null, Ho: <3.2
alternate, H1: >3.2
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.655
since our test is right-tailed
reject Ho, if to > 1.655
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =4-3.2/(2/sqrt(150))
to =4.899
| to | =4.899
critical value
the value of |t | with n-1 = 149 d.f is 1.655
we got |to| =4.899 & | t | =1.655
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 4.899 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: <3.2
alternate, H1: >3.2
right tailed test
test statistic: 4.899
critical value: 1.655
decision: reject Ho
p-value: 0
no evidence to vallidate americans watch less than 3.2 hours of television per day
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