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

Answer 1

Answer:

Option a) 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.        

Step-by-step explanation:

We are given the following information in the question:

$H_{0}: \mu \leq \ 3,200\\H_A: \mu > \ 3,200$

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 also known as a “false positive” and is the error of rejecting a null  hypothesis when it is actually true.
• In other words, this is the error of accepting an  alternative hypothesis when the results can be  attributed by null hypothesis.
• A type I error occurs during the hypothesis testing process when a null hypothesis is rejected, even though it is correct and should not be rejected.

Thus, in the above hypothesis type  error will occur when we reject the null hypothesis even when it is true.

Option a) 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.