Suppose the true team of an incoming lot of steel bars is 10, 038 psi. What is t

Question

Suppose the true team 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 deviation was $80. Using a significance level of .05, test whether the average grocery bill is $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: =300
alternate, H1: !=300
level of significance, = 0.05
from standard normal table, two tailed t /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 | with n-1 = 399 d.f is 1.966
we got |to| =3.75 & | t | =1.966
make decision
hence value of | to | > | t | 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: =300
alternate, H1: !=300
test statistic: -3.75
critical value: -1.966 , 1.966
decision: reject Ho
p-value: 0.0002

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