Question

You wish to test the following claim (Ha) at a significance level of α=0.05.

      Ho:μ=62.6
      Ha:μ<62.6

You believe the population is normally distributed and you know the standard deviation is σ=10. You obtain a sample mean of M=59.5 for a sample of size n=33.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

in the critical region

not in the critical region

This test statistic leads to a decision to...

reject the null

accept the null

fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population mean is less than 62.6.

There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 62.6.

The sample data support the claim that the population mean is less than 62.6.

There is not sufficient sample evidence to support the claim that the population mean is less than 62.6.

Answer 1

Given that,
population mean(u)=62.6
standard deviation, sigma =10
sample mean, x =59.5
number (n)=33
null, Ho: μ=62.6
alternate, H1: μ<62.6
level of significance, alpha = 0.05
from standard normal table,left tailed z alpha/2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 59.5-62.6/(10/sqrt(33)
zo = -1.781
| zo | = 1.781
critical value
the value of |z alpha| at los 5% is 1.645
we got |zo| =1.781 & | z alpha | = 1.645
make decision
hence value of | zo | > | z alpha| and here we reject Ho
p-value : left tail - ha : ( p < -1.781 ) = 0.037
hence value of p0.05 > 0.037, here we reject Ho
ANSWERS
---------------
null, Ho: μ=62.6
alternate, H1: μ<62.6
test statistic: -1.781
critical value: -1.645
decision: reject Ho
p-value: 0.037
we have enough evidence to support the claim that the population mean is less than 62.6