Question

According to the document Consumer Expenditures, a publication of the U.S. Bureau of Labor Statistics, the average consumer unit spent $1749 on apparel and services in 2002. That same year, 25 consumer units in the Northeast had the following normally distributed annual expenditures, in dollars, on apparel and services. At the 5% significance level, do the data provide sufficient evidence to conclude that the 2002 mean annual expenditure on apparel and services for consumer units in the Northeast differed from the national mean of $1749? (Note: The sample mean and sample standard deviation of the data are $1935.76 and $350.90, respectively.)  Check the assumptions  Hypotheses  Sample mean: Sample Std. dev: Sample size: Significance level:  P-value = Conclusion: Since P-value is ___________ than the significant level, _________, we ____________ null hypothesis. We have sufficient evidence to say that...

Answer 1

Given that,
population mean(u)=1749
sample mean, x =1935.76
standard deviation, s =350.9
number (n)=25
null, Ho: μ=1749
alternate, H1: μ!=1749
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.064
since our test is two-tailed
reject Ho, if to < -2.064 OR if to > 2.064
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =1935.76-1749/(350.9/sqrt(25))
to =2.6612
| to | =2.6612
critical value
the value of |t α| with n-1 = 24 d.f is 2.064
we got |to| =2.6612 & | t α | =2.064
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 2.6612 ) = 0.0137
hence value of p0.05 > 0.0137,here we reject Ho
ANSWERS
---------------
null, Ho: μ=1749
alternate, H1: μ!=1749
test statistic: 2.6612
critical value: -2.064 , 2.064
decision: reject Ho
p-value: 0.0137
we have enough evidence to support the claim that the 2002 mean annual expenditure on apparel and services for consumer units in the Northeast differed from the national mean of $1749