Question

Which is cheaper: eating out or dining in? The mean cost of a flank steak, broccoli, and rice bought at the grocery store is $13.04. A sample of 100 neighborhood restaurants showed a mean price of $12.65 and a standard deviation of $2 for a comparable restaurant meal. (a) Choose the appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean cost of a restaurant meal is less than fixing a comparable meal at home. H0: - Select your answer -µ > 13.04µ ≤ 13.04µ < 13.04µ ≥ 13.04Item 1 Ha: - Select your answer -µ > 13.04µ ≤ 13.04µ < 13.04µ ≥ 13.04Item 2 (b) Using the sample from the 100 restaurants, what is the p value? If required, round your answer to four decimal places. (c) At α = 0.05, what is your conclusion? We - Select your answer -rejectfail to rejectItem 4 the null hypothesis. We - Select your answer -cancannotItem 5 conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.

Answer 1

Given that,
population mean(u)=13.04
sample mean, x =12.65
standard deviation, s =2
number (n)=100
null, Ho: μ=13.04
alternate, H1: μ<13.04
level of significance, α = 0.05
from standard normal table,left tailed t α/2 =1.66
since our test is left-tailed
reject Ho, if to < -1.66
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =12.65-13.04/(2/sqrt(100))
to =-1.95
| to | =1.95
critical value
the value of |t α| with n-1 = 99 d.f is 1.66
we got |to| =1.95 & | t α | =1.66
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :left tail - Ha : ( p < -1.95 ) = 0.027
hence value of p0.05 > 0.027,here we reject Ho
ANSWERS
---------------
a.
null, Ho: μ=13.04
alternate, H1: μ<13.04
test statistic: -1.95
critical value: -1.66
decision: reject Ho
b.
p-value: 0.027
c.
we have enough evidence to support the claim that mean cost of restaurant meal is less than fixing a comparable meal at home