A sample of 16 cookies is taken to test the claim that each cookie contains at l

Question

A sample of 16 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips. The average number of chocolate chips per cookie in the sample was 7.875 with a standard deviation of 2. Assume the distribution of the population is normal. Let mu denote the average number of chocolate chips in all the cookies. The hypothesis to test the claim is: H_{0}:geq 9 , H_{a}: u< 9 geq 9 , H_{a}: u< 9 .

a) what is the test statistic

b) the critical value for this test at a 0.5 level of significance is

c) the p-value for this test statistic is

d) at a 0.5 level of significance, it can be concluded that the mean of the population is

Explanation / Answer

Given that,
population mean(u)=9
sample mean, x =7.875
standard deviation, s =2
number (n)=16
null, Ho: >=9
alternate, H1: <9
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.753
since our test is left-tailed
reject Ho, if to < -1.753
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =7.875-9/(2/sqrt(16))
to =-2.25
| to | =2.25
critical value
the value of |t | with n-1 = 15 d.f is 1.753
we got |to| =2.25 & | t | =1.753
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -2.25 ) = 0.01994
hence value of p0.05 > 0.01994,here we reject Ho
ANSWERS
---------------
null, Ho: >=9
alternate, H1: <9
test statistic: -2.25
critical value: -1.753
decision: reject Ho
p-value: 0.01994

we don't have evidence that it has mean rate atleast nine

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