# Finding the P-Value for Hypothesis Testing

• Kerrie
In summary, the conversation discusses a homework problem involving finding the P-value for testing a claim about standard deviations. The problem involves determining if a mutual fund has moderate risk based on its standard deviation of monthly returns. The t-test function on the TI-84 Plus calculator is not applicable in this scenario. The conversation also mentions using a normal probability plot and various methods for computing the P-value. A suggestion is made to search for "hypothesis test for variance" and use online Chi-squared calculators as modern tools to solve the problem.
Kerrie
Staff Emeritus
Gold Member

## 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?

Kerrie said:

## 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".

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.

Kerrie said:
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?

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.

The invNorm also requires the mean.

Kerrie said:
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.

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

Greg Bernhardt

## 1. What is a "P-Value" in hypothesis testing?

The P-Value, or probability value, is a statistical measure used in hypothesis testing to determine the likelihood of obtaining the observed results or results more extreme, assuming that the null hypothesis is true. It is often used to assess the strength of evidence against the null hypothesis.

## 2. How do you calculate the P-Value for hypothesis testing?

The P-Value can be calculated using various statistical methods, depending on the type of hypothesis test being conducted. In general, it involves determining the probability of obtaining the observed data or data more extreme, given the assumptions of the null hypothesis. This can be done using statistical software or by referring to a P-Value table.

## 3. What does a small P-Value indicate in hypothesis testing?

A small P-Value, typically less than 0.05, indicates that the observed results are unlikely to occur if the null hypothesis is true. This suggests that there is strong evidence against the null hypothesis, and it may be rejected in favor of the alternative hypothesis. However, it is important to consider the context and potential limitations of the study before making conclusions.

## 4. What does a large P-Value indicate in hypothesis testing?

A large P-Value, typically greater than 0.05, indicates that the observed results are likely to occur if the null hypothesis is true. This suggests that there is not enough evidence to reject the null hypothesis and accept the alternative hypothesis. However, it is important to note that a larger sample size may result in a smaller P-Value, so the interpretation of a large P-Value should be considered in the context of the study.

## 5. What is the significance level in hypothesis testing and how does it relate to the P-Value?

The significance level, often denoted as α (alpha), is the predetermined threshold used to determine whether the P-Value is small enough to reject the null hypothesis. A common significance level is 0.05, which means that if the P-Value is less than 0.05, the null hypothesis will be rejected. The significance level and P-Value are inversely related; a smaller significance level requires a smaller P-Value to reject the null hypothesis, and vice versa.

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