Using the numerical data for your team project, conduct a two sample, two-tailed hypothesis test for the mean, with a 0.05 level of significance. Find and interpret each step.
H0:
H1:
Test statistic =
Critical value =
p-value =
Reject the null hypothesis or do not reject the null hypothesis?
What does this mean?
For example:
H0: ƒÊX = ƒÊY
The mean (average) gas price in city X equals the mean (average) gas price in city Y during January 2012.
H1: ƒÊX �‚ ƒÊY
The mean (average) gas price in city X does not equal the mean (average) gas price in city Y during January 2012.
To conduct a two-sample, two-tailed hypothesis test for the mean with a 0.05 level of significance, follow these steps:
Step 1: State the null and alternative hypotheses (H0 and H1)
- H0 (Null Hypothesis): The two population means are equal.
- H1 (Alternative Hypothesis): The two population means are not equal.
For the example, the hypotheses would be:
H0: ƒÊX = ƒÊY
H1: ƒÊX �‚ ƒÊY
Step 2: Determine the test statistic
The test statistic for a two-sample, two-tailed hypothesis test for the mean is the t-statistic calculated using the sample means, sample standard deviations, and sample sizes of the two groups.
Step 3: Decide on a significance level (alpha)
In this case, the significance level is given as 0.05, which means that we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is true).
Step 4: Calculate the critical value
To find the critical value, you need to consult the t-distribution table or use software/tools that can calculate it based on the degrees of freedom and desired significance level. The critical value helps you determine the cutoff points for rejecting or failing to reject the null hypothesis.
Step 5: Calculate the p-value
The p-value is the probability of observing a sample mean difference as extreme as the one calculated or more extreme, assuming that the null hypothesis is true. It allows you to determine the strength of the evidence against the null hypothesis.
Step 6: Compare the test statistic with the critical value and the p-value
- If the test statistic falls within the critical value range, fail to reject the null hypothesis.
- If the test statistic falls outside the critical value range, reject the null hypothesis.
Step 7: Interpret the results
If the null hypothesis is rejected, it means that there is evidence to suggest that the two population means are not equal. On the other hand, if the null hypothesis is not rejected, it suggests that there is not enough evidence to conclude that the two population means differ.
Note: The specific formulas for calculating the test statistic, critical value, and p-value depend on the specific type of test (e.g., independent samples t-test, paired samples t-test). It is important to use the appropriate formula based on the characteristics of your data and the assumptions of the specific statistical test being used.