Show all of your work. Answers without work or an adequate explanation will rece
ID: 3218019 • Letter: S
Question
Show all of your work. Answers without work or an adequate explanation will receive no credit. Partial credit awarded when appropriate Zstat = (X - mu)/(sigma)/Squareroot n, tsat = (X - mu)/(s)/Squareroot n, Zstat = (phat - P)/Squareroot pq/n Consumer Retorts, a leading consumer magazine, claims that the small pizza's served at Vinnie Gumba's Pizza Joint are not 12 inches in diameter. A random sample of 16 pizzas' yields the following results: The sample mean equals 11.75 inches The sample standard deviation equals 0.5 inches 4 people (out of 16) ordered the "Gumba Special", pizza (pineapple, anchovies, and garlic) a. Test the hypothesis that the true population mean of a small pizza is less than 12 inches. Set the Type 1 error equal to 1%. b. Test the hypothesis that the true population means of a small pizza is not equal to 12 inches. Set the Type 1 error equal to 10%. c. Test the hypothesis that the true population proportion for ordering the "Gumba Special" is greater than 0.20. Set the Type 1 error equal to 5%.Explanation / Answer
PART A.
Given that,
population mean(u)=12
sample mean, x =11.75
standard deviation, s =0.5
number (n)=4
null, Ho: >12
alternate, H1: <12
level of significance, = 0.01
from standard normal table,left tailed t /2 =4.541
since our test is left-tailed
reject Ho, if to < -4.541
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =11.75-12/(0.5/sqrt(4))
to =-1
| to | =1
critical value
the value of |t | with n-1 = 3 d.f is 4.541
we got |to| =1 & | t | =4.541
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :left tail - Ha : ( p < -1 ) = 0.1955
hence value of p0.01 < 0.1955,here we do not reject Ho
ANSWERS
---------------
null, Ho: =12
alternate, H1: <12
test statistic: -1
critical value: -4.541
decision: do not reject Ho
p-value: 0.1955
no, its nt less than 12