You must do Problem 1. Please do any 4 of the remaining 6 problems. Suppose the

Question

You must do Problem 1. Please do any 4 of the remaining 6 problems. Suppose the true mean of an incoming lot of steel bars is 10, 038 psi. What is the probability that the quality control inspector will accept the bars as having a " true " mean of 10,000 psi. What is the probability of making a type II error? The number of observations in the sample is 100. The standard deviation is 400 psi. Choose a confidence interval of 95%. A supermarket chain is doing research in the City of Cerritos to determine whether average monthly household grocery bill is $300. Supermarket personnel took a sample size 400. They found that the sample mean was $285 and the sample standard deviate was $80. Using a significance level of .05, test whether the average grocery bill $300. Check your answer using the p-value test.

Explanation / Answer

Q2.
Given that,
population mean(u)=300
sample mean, x =285
standard deviation, s =80
number (n)=400
null, Ho: µ=300
alternate, H1: µ!=300
level of significance, a = 0.05
from standard normal table, two tailed t a/2 =1.966
since our test is two-tailed
reject Ho, if to < -1.966 OR if to > 1.966
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =285-300/(80/sqrt(400))
to =-3.75
| to | =3.75
critical value
the value of |t a| with n-1 = 399 d.f is 1.966
we got |to| =3.75 & | t a | =1.966
make decision
hence value of | to | > | t a| and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -3.75 ) = 0.0002
hence value of p0.05 > 0.0002,here we reject Ho
ANSWERS
---------------
null, Ho: µ=300
alternate, H1: µ!=300
test statistic: -3.75
critical value: -1.966 , 1.966
decision: reject Ho
p-value: 0.0002
we don't have evidence to support the grocery bill is 300

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