Question
In: Statistics and Probability
A random sample of 50 measurements resulted in a sample mean of 62 with a sample...
A random sample of 50 measurements resulted in a sample mean of 62 with a sample standard deviation 8. It is claimed that the true population mean is at least 64.
a) Is there sufficient evidence to refute the claim at the 2% level of signifigance?
b) What is the p-vaule?
c) What is the smallest value of alpha for which the claim will be rejected?
Solutions
Expert Solution
a. Here claim is that mean is atleast 64.
Now as we know null hypothesis is always with equality sign.
and so 
As n>30, we will use z test statistics
The z-critical value for a left-tailed test, for a significance level of ?=0.02 is
zc?=?2.05
Graphically
As z statistics is not in the rejection region we fail to reject the null hypothesis.
Hence the claim is not rejected
b. P value is 
c. As P value is 0.0384 so alpha value of 0.04 i.e. 4% will serve as to reject the claim.
orchestra answered 1 year agoRelated Solutions
A random sample of 50 measurements resulted in a sample mean of 62 with a sample standard deviation 8. It is claimed that the true population mean is at least 64.
A random sample of 50 measurements resulted in a sample mean of 62 with a sample standard deviation 8. It is claimed that the true population mean is at least 64.(a) Is there sufficient evidence to refute the claim at the 2% level of significance?(b) What is the p-value?(c) What is the smallest value of α for which the claim will be rejected?
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