Question

The mean annual return for an employee's IRA is at most 4.7 percent.

A) Write the null and alternative hypotheses.

B) Indicate whether the hypothesis is left,right, two-tailed.

Step 1

**Hypothesis:**

Hypothesis is an assumption about the parameter of the population which will be made on the limited evidence as the start value to proceed for further investigation, and the assumption may or may not be true.

In testing the hypothesis is of two types. The two types are:

- Null hypothesis (
*H*)_{0} - Alternative hypothesis (
*H*)_{1}

*Null and alternative hypothesis:*

*Null hypothesis:*

Null hypothesis is a statement which is tested for statistical significance in the test. The decision criterion indicates whether the null hypothesis will be rejected or not in the favour of alternate hypothesis. In other words it can be said that, the null hypothesis is a statement which indicates the relationship between statistical measurements, distributions or categories. More often, null hypothesis states no significance relationship between variables or populations. But, null does not indicate “0” all the time.

*Alternate hypothesis:*

Alternate hypothesis is contradictory statement of the null hypothesis. The alternate hypothesis represents whether the hypothesis test is one tailed or two tailed.

- If the alternate hypothesis indicates “not equal to” symbol then the hypothesis test is said to be two tailed.
- If the alternate indicates “less than” symbol then the hypothesis test is said to be left tailed.
- If the alternate hypothesis indicates “greater than” symbol then the hypothesis test is said to be right tailed.

Step 2

**A.**

**State the appropriate hypothesis:**

It is given that, the mean annual rate for an employee’s IRA is at most 4.7 percent.

*The hypotheses are given below:*

*Null hypothesis:*

*H*_{0} : μ ≤ 4.7 percent

That is, the mean annual rate for an employee’s IRA is at most 4.7 percent.

*Alternative hypothesis:*

*H*_{a} : μ > 4.7 percent

That is, the mean annual rate for an employee’s IRA is greater than 4.7 percent.

Step 3

**B.**

**Indicate whether the hypothesis is left tailed or right tailed or two tailed:**

Since, the alternate hypothesis indicates “greater than&rdquo...

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