Finding the P-Value for Hypothesis Testing

[Kerrie]

Homework Statement

Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 6%. A mutual-fund rating agency randomly selects 28 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 5.23%. Is there sufficient evidence to conclude that the fund has moderate risk at the α=0.05 level of significance? A normal probability plot indicates that the monthly rates of return are normally distributed.

Homework Equations

This homework problem has multi-answers, but I am struggling to find the P-value with Hypothesis Testing when testing a claim about a standard deviation or variance. The homework question (online class) is asking to solve the P-value using technology. I have a TI-84 Plus calculator. I also have StatCrunch (the program within the online course), but not StatDisk.

The Attempt at a Solution

I have used the T-Test function in the calculator when testing the mean, but I don't have the mean in this problem to input for the T-Test. Test Statistic is X² = 20.515 (rounded).

I understand what the P-value is for, but it seems there are various methods on the calculator to compute it. Is there anyone with knowledge of the TI-84 plus to find the P-value for testing a claim about standard deviations?

 

[Ray Vickson]

Homework Statement

Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 6%. A mutual-fund rating agency randomly selects 28 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 5.23%. Is there sufficient evidence to conclude that the fund has moderate risk at the α=0.05 level of significance? A normal probability plot indicates that the monthly rates of return are normally distributed.

Homework Equations

This homework problem has multi-answers, but I am struggling to find the P-value with Hypothesis Testing when testing a claim about a standard deviation or variance. The homework question (online class) is asking to solve the P-value using technology. I have a TI-84 Plus calculator. I also have StatCrunch (the program within the online course), but not StatDisk.

The Attempt at a Solution

I have used the T-Test function in the calculator when testing the mean, but I don't have the mean in this problem to input for the T-Test. Test Statistic is X² = 20.515 (rounded).

I understand what the P-value is for, but it seems there are various methods on the calculator to compute it. Is there anyone with knowledge of the TI-84 plus to find the P-value for testing a claim about standard deviations?

The t-distribution is never the correct one to use when testing variance. Do a search on "hypothesis test for variance".

 

[Kerrie]

Already looked at various sites, but most of the PDF's require the mean. I'll admit that I have struggled with this statistics course, but I have usually found help by doing an online search. Hoping I can get help here as I am really stuck.

 

[Ray Vickson]

Already looked at various sites, but most of the PDF's require the mean. I'll admit that I have struggled with this statistics course, but I have usually found help by doing an online search. Hoping I can get help here as I am really stuck.

The usual test for variance does NOT need to know the mean. I cannot offer more hints until you explain in more detail what you have done already; for example: what tests have you looked at?

 

[Kerrie]

I have looked at the Chi-Square Distribution table, but it only has a few areas that don't go below .90. My text gives very little information on calculator functions, I have very diligent notes on my calculator functions, but I cannot find the function to use. I thought the X² test would work, but the book does not show that test as an option. I can't use the Z interval test, again it needs the mean.

 

[Kerrie]

The invNorm also requires the mean.

 

[Ray Vickson]

I have looked at the Chi-Square Distribution table, but it only has a few areas that don't go below .90. My text gives very little information on calculator functions, I have very diligent notes on my calculator functions, but I cannot find the function to use. I thought the X² test would work, but the book does not show that test as an option. I can't use the Z interval test, again it needs the mean.

I bet you can find on-line Chi-squared calculators, so using modern tools you can do much more than appears in your book.

 

[Kerrie]

Thank you, this little bit of guidance was all I needed. Found one that will at least help with the homework.