Question

A sample of 46 observations is selected from a normal population. The sample mean is 39, and the population standard deviation is 9.

Conduct the following test of hypothesis using the 0.10 significance level.

*H*_{0} : μ ≤ 38

*H*_{1} : μ > 38

**a.** Is this a one- or two-tailed test?

(Click to select) (One-tailed test / Two-tailed test)

**b.** What is the decision rule? **(Round
the final answer to 3 decimal places.)**

(Click to select) (Reject /
Accept) *H*_{0} and (Click to
select) (accept / reject) *H*_{1} when
*z* > .______________

**c.** What is the value of the test statistic?
**(Round the final answer to 2 decimal places.)**

Value of the test statistic ___________

**d.** What is your decision regarding
*H*_{0}?

(Click to select) (Reject / Do not
reject) *H*_{0}.

There is (Click to select) (not enough / enough) evidence to conclude that the population mean is greater than 38.

**e.** What is the *p*-value? **(Round
the final answer to 4 decimal places.)**

__________________

Answer #1

a) As we are testing here whether the mean is more than 38,
**therefore this is a case of a one tailed test
here.**

b) For 0.1 level of significance, we have from the standard
normal tables:

P(Z > 1.282) = 0.1

Therefore the decision rule here is given as:

**Reject H0 if z > 1.282**

c) The test statistic here is computed as:

**Therefore 0.7536 is the test statitistic value
here.**

d) As the test statistic value is less than the critical z
value, **therefore Do not reject H0 is the correct answer
here.** Therefore is not enough evidence here to conclude
that the population mean is greater than 38.

e) As this is a one tailed test, the p-value here is computed from the standard normal tables as:

p = P(Z > 0.7536) = 0.2255

**Therefore 0.2255 is the required p-value
here.**

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