Solving Statistics Questions: Alex’s Answers

[PARAJON]

HI group, I was wondering if someone can check my answers to see if I'm right on the following questions. Thanks!

Alex



1.) The 95% confidence interval states that 95% of the sample means of a specified sample size selected from a population will lie within plus and minus 1.96 standard deviations of the hypothesized population mean.

a.) True
b.) False


My answer: False (population mean lies within the interval)

2.) If the null hypothesis that two means are equal is true, where will 97% of the computed z- values lie between?

a.) +- 2.58
b.) +- 2.33
c.) +- 2.17
d.) +- 2.07
e.) none of the above.

My answer: e : none of the above

3.) If the confidence interval includes 0, there is no difference in the pair of treatment means.

a.) Ture
b.) False

My answer: False

 

[HallsofIvy]

You don't give any reason for your answers so I can't tell where you have gone wrong but you certainly have!

"1.) The 95% confidence interval states that 95% of the sample means of a specified sample size selected from a population will lie within plus and minus 1.96 standard deviations of the hypothesized population mean.

a.) True
b.) False


My answer: False (population mean lies within the interval)"

The question didn't ask about the population mean, it asked about the sample mean. The statement given is true and is, simply, the definition of "95% confidence interval". Check the definition in your book.

".) If the null hypothesis that two means are equal is true, where will 97% of the computed z- values lie between?

a.) +- 2.58
b.) +- 2.33
c.) +- 2.17
d.) +- 2.07
e.) none of the above.

My answer: e : none of the above"

How did you arrive at that? Checking a table of Normal Distribution values, I find that the area under the normal curve, from 0 to 2.17, is .485 which is .97/2. Because of the symmetry of the curve, 97% of the area is between -2.17 and 2.17, answer c.

"3.) If the confidence interval includes 0, there is no difference in the pair of treatment means.

a.) True
b.) False

My answer: False"

I'm not crazy about the question itself and would be willing to accept "false" based on the wording. If the confidence interval includes 0, then one cannot REJECT the null hypothesis that there is "no difference in the pair of treatment means" but that is NOT the same as saying there IS no difference!

 

[tacman]

(the confidence interval does not determine if there is a difference, it just shows the range of values in which the true difference between the means may lie)