Question

Step 1

**Hypotheses:**

*Null hypothesis:*

*H*_{0}: *µ* ≤ 1,500

*Alternative hypothesis:*

*H*_{1}: *µ* > 1,500

Since the alternative hypothesis states *µ* > 1,500, this test is a **right-tailed** test.

**Critical value:**

Consider the level of significance as 0.05.The critical value for 0.05 significance level is 1.96.

Step 2

**Calculation:**

It is given that *X *has a normal distribution and *σ* = 250.

Since it is assumed that *X *has a normal distribution with known *σ*, the standard normal is the appropriate sampling distribution.

*Test statistic for z-test:*

Here, the sample mean, *x*-bar is 1,650.

Population mean, *µ* is 1,500.

Population standard deviation, *σ* = 250.

Sample size, *n* is 100.

The test statistic for *z*-test is calculated as **6** from the calculations given below.

Step 3

*Computation of P-value:*

The *P*-value for the *z*-test can be obtained using the excel formula,** “**=NORM.S.DIST(6,TRUE)” and is 1.00.

Th...

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