Question

Although your product, a word game, has a list price of $12.95, each store is free to set the price as it wishes. You have just completed a quick survey, and the marked prices at a random sample of stores that sell the product were as follows: $12.95, 9.95, 8.95, 12.95, 12.95, 9.95, 9.95, 9.98,13.00,9.95

a) Estimate the mean selling price you would have found had you been able to survey all stores selling your product.

b) for a typical store, approximately how different is the actual selling price from the average.

c) your marketing department believes that the games generally sell at a mean discount of 12% from the list price. Identify the hypotheses you would work with to test the population mean selling price against this belief.

d) Test the hypotheses from part c.

Answer 1

Given that,
population mean(u)=12.95
sample mean, x =11.058
standard deviation, s =1.581
number (n)=10
null, Ho: μ=12.95
alternate, H1: μ!=12.95
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.262
since our test is two-tailed
reject Ho, if to < -2.262 OR if to > 2.262
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =11.058-12.95/(1.581/sqrt(10))
to =-3.7843
| to | =3.7843
critical value
the value of |t α| with n-1 = 9 d.f is 2.262
we got |to| =3.7843 & | t α | =2.262
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -3.7843 ) = 0.0043
hence value of p0.05 > 0.0043,here we reject Ho
ANSWERS
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a.
the mean selling price you would have found had you been able to survey all stores selling your product.
sample mean, x =11.058
standard deviation, s =1.581
number (n)=10
b.
standard normal distribution approximately
null, Ho: μ=12.95
alternate, H1: μ!=12.95
c.
test statistic: -3.7843
critical value: -2.262 , 2.262
decision: reject Ho
p-value: 0.0043
d.
we have enough evidence to support the claim that the games generally sell at a mean discount of 12% from the list price is 12.95$.