# Hypothesis Tests Comparing Two Means - …

When testing hypotheses about a mean or mean difference, a t-distribution is used to find the p-value. This is a close cousin to the normal curve. T-Distributions are indexed by a quantity called degrees of freedom, calculated as df = n – 1 for the situation involving a test of one mean or test of mean difference.

## Hypothesis Testing For a Sample Mean - LTCC Online

### Hypothesis test for difference of means (video) | Khan …

The p-value is p = 0.019. This is below the .05 standard, so the result is statistically significant. This means we decide in favor of the alternative hypothesis. We're deciding that the population mean is not 72.

### Lesson 12: Hypothesis Testing for a Population Mean

The p-value is p = 0.236. This is not below the .05 standard, so we do not reject the null hypothesis. Thus it is possible that the true value of the population mean is 72. The 95% confidence interval suggests the mean could be anywhere between 67.78 and 73.06.

## represents the run of 100 coin flips

The first step is to state the hypothesis to be tested, called the null hypothesis, and the alternative hypothesis. In this example, upper-level management wants to know if there is a difference in the mean amounts purchased on impulse at the two stores. An alternative way to state this question is "Is the mean amount purchased on impulse at the First Street store equal to the mean amount purchased at the Main street store?" Recall that the "equality" part of the hypothesis is always stated in the null hypothesis. Therefore, the null and alternative hypotheses for this example are:

## Say you have a set of observations O and a null hypothesis H 0

We decide: "The data (and its sample mean) are significantly different than the value of the mean hypothesized under the null hypothesis, at the .01 level of significance." This decision is likely to be wrong (Type I error) 1 time out of 100.

## Excel Regression Analysis | R Squared | Goodness of Fit

SolutionWe first develop the hypothesesNext we need to find the standard deviation. Recall from ,we had that the mean of the difference is and the standard deviation is Wecan substitute the sample means and sample standard deviations for a pointestimate of the population means and standard deviations. We have Now we can calculate the t-score. We haveTo calculate the degrees of freedom, we can take the smaller of the two numbers and. So in this example we use degrees of freedom. The t-table gives a value of for the value
Hypothesis Testing For a Difference Between Means for Samples Using Pooled Standard Deviations (Optional)Recall that for small samples we need to make the followingassumptions:

### SIX SIGMA Glossary: Hypothesis Tests for Means

(Use) SolutionWe write:We have: so that and Thet-critical value corresponding to with degrees of freedom is which is greater than. Hence we fail to reject the null hypothesis and conclude that there is not sufficient evidence to suggest that there is a difference between the mean starvation time for cats and dogs.

### Test of hypothesis for difference between means - …

If the P-value is greater than α, do not reject the null hypothesis. In our example concerning the mean grade point average, suppose that our random sample of n = 15 students majoring in mathematics yields a test statistic t* equaling 2.5.

### What is the Scientific Method and why is it important?

Common significance levels are .10, .05, and .01. Suppose you chose a .05 level of significance, meaning there is a 5% chance that you will reject the null hypothesis when it is true.