Q1-3BSC - Elementary Statistics

Question

A formal hypothesis test is to be conducted using the claim that the mean height of men is equal to 174.1 cm.

a. What is the null hypothesis, and how is it denoted? 

b. What is the alternative hypothesis, and how is it denoted?

c. What are the possible conclusions that can be made about the null hypothesis?

d. Is it possible to conclude that “there is sufficient evidence to support the claim that the mean height of men is equal to 174.1 cm”?

Step-by-Step Solution

Answer

a.The null hypothesis states that the mean height of men is equal to 174.1 cm. It is denoted in the following manner:

\({H_0}:\mu  = 174.1\)

 

b. The alternative hypothesis states that the mean height of the mean is not equal to 174.1 cm. It is denoted in the following manner:

\({H_1}:\mu  \ne 174.1\)

 

c. The two possible conclusions are as follows:

• The null hypothesis is rejected;that is, the claim that the mean height of men is equal to 174.1 cm is rejected.
• The null hypothesis is failed to reject;that is, the claim that the mean height of men is equal to 174.1 cm is failed to reject.

 

d. Since it is not possible to support/accept the claim made under the null hypothesis, it is not possible to conclude that “there is sufficient evidence to support the claim that the mean height of men is equal to 174.1 cm.”

Step 1: Given information

It is claimed that the mean height of men is equal to 174.1 cm.

Step 2: Hypotheses

Let \(\mu \) denote the population mean height of men.

 

a.

 

Null hypothesis: The mean height of men is equal to 174.1 cm.

It is denoted in the following manner:

\({H_0}:\mu  = 174.1\)

 b.

 

Alternative hypothesis: The mean height of men is not equal to 174.1 cm.

\({H_1}:\mu  \ne 174.1\)

Step 3: Conclusions about the null hypothesis

c.

 

Two possible conclusions can be made about the null hypothesis:

• Rejection of the null hypothesis or rejection of the claim that the mean height of men is equal to 174.1 cm
• Failure of rejection of the null hypothesis or failure of rejection of the claim that the mean height of men is equal to 174.1 cm

 

It should be noted that the claim made under the null hypothesis can never be supported or accepted.

 

d.

 

Since the claim made under the null hypothesis cannot be supported, it is not possible to conclude that “there is sufficient evidence to support the claim that the mean height of men is equal to 174.1 cm.”