Answer b and c Show all of your work. Answers without worn or an adequate explan

Question

Answer b and c Show all of your work. Answers without worn or an adequate explanation will receive no credit Partial credit awarded when appropriate. Zstat = (X - mu)/(sigma)/Squareroot n, tstat = (x - mu)/(s)/Squareroot n, = (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 I 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 I error equal to 10%. c. Test the hypothesis that the true population proportion for ordering the -"Gumba Specials" is greater than 0.20 Set the Type I error equal to 5%

Explanation / Answer

PART B.
Given that,
population mean(u)=12
standard deviation, =0.5
sample mean, x =11.75
number (n)=4
null, Ho: =12
alternate,small pizza is not equal to 12 H1: !=12
level of significance, = 0.1
from standard normal table, two tailed z /2 =1.645
since our test is two-tailed
reject Ho, if zo < -1.645 OR if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 11.75-12/(0.5/sqrt(4)
zo = -1
| zo | = 1
critical value
the value of |z | at los 10% is 1.645
we got |zo| =1 & | z | = 1.645
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != -1 ) = 0.31731
hence value of p0.1 < 0.31731, here we do not reject Ho
ANSWERS
---------------
null, Ho: =12
alternate, H1: !=12
test statistic: -1
critical value: -1.645 , 1.645
decision: do not reject Ho
p-value: 0.31731
we have evidence to support size is 12

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