Question

Suppose that you are testing the hypotheses H0​: u=74 vs. HA​: u does not equal 74. A sample of size 51 results in a sample mean of 69 and a sample standard deviation of 1.8. ​

a) What is the standard error of the​ mean? ​

b) What is the critical value of​ t* for a 90​% confidence​ interval?

​c) Construct a 90​% confidence interval for mu. ​

d) Based on the confidence​ interval, at a=0.100 can you reject H0​? Explain.

Answer 1

null and alternative hypothesis is

Ho:   = 74

Ha:   74

n= 51,   = 69  , s= 1.8

c= 90%

a)

formula for standard error of the​ mean

= 0.25205

Standard error of the​ mean = 0.25205

b)

find the t critical value for c=90% with df=n-1 = 51-1 = 50

using t table we get critical value as

Critical value = 1.676

c)

formula for confidence interval is

68.578 <    < 69.422

thus we get confidence interval as

( 68.578 , 69.422 )

d)

claim is 74

from above confidence interval we find that we find that 74 do not lies within our calculated confidence interval 68.578 to 69.422.

Hence, mean is different from 74.

Yes, we can reject the claim that mean is not equal to 74