Question

Which of the following represents a Type I error for the null and alternative hypotheses H0: μ ≤ $3,200 and Ha: μ > $3,200, where μ is the average amount of money in a savings account for a person aged 30 to 40?

a. A Type I error would occur if we fail to reject H0 and conclude that the average amount is $3,200 or less when in fact the average amount is greater than $3,200.
b. A Type I error would occur if we reject H0 and conclude that the average age is less than 30 when in fact the average age is greater than 40.
c. A Type I error would occur if we fail to reject H0 and conclude that the average amount is less than or equal to $3,200 when in fact the average amount is $3,200 or less.

Answer 1

Type I error would occur if we reject null hypothesis and conclude that the average amount is greater than $3,200 when in fact the average amount is $3,200 or less.

Explanation:

We are given the following information in the question:

The null and alternative hypotheses:

`H_(0): \mu \leq \$3,200\\H_A: \mu > \$3,200`

where μ is the average amount of money in a savings account for a person aged 30 to 40.

Type I error:

• Type I error is the error when we reject the null hypothesis when it is true.
• It is also known as false positive.

Thus, for the given hypothesis test type I error is represented as:

Type I error would occur if we reject null hypothesis and conclude that the average amount is greater than $3,200 when in fact the average amount is $3,200 or less.