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?
To conduct a two sample, two-tailed hypothesis test for the mean, you'll need the following information:
H0: The null hypothesis states that there is no significant difference between the means of the two samples.
H1: The alternative hypothesis states that there is a significant difference between the means of the two samples.
Level of significance: 0.05 (meaning that we are willing to accept a 5% chance of making a Type I error, which is rejecting the null hypothesis when it is true.)
To find and interpret each step, follow these steps:
Step 1: Calculate the sample means and standard deviations for the two samples.
- Let's call the means of the two samples as x1 and x2.
- Calculate the standard deviations of the two samples as s1 and s2.
Step 2: Conduct the hypothesis test.
- Calculate the test statistic, which depends on the type of hypothesis test being performed. For a two sample t-test, the test statistic is typically the t-value.
- Use the formula for the t-value: t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2)), where n1 and n2 are the sample sizes.
- Calculate the t-value using the formula above.
Step 3: Find the critical value(s) or p-value.
- For a two-tailed test, divide the level of significance (0.05) by 2 to get an alpha value of 0.025 for each tail.
- Look up the critical value(s) from the t-distribution table based on the degrees of freedom (df), which can be calculated as (n1 + n2 - 2) if the sample sizes are equal.
- Alternatively, you can use statistical software or calculators to find the critical value(s) or p-value directly.
Step 4: Interpret the results.
- If the absolute value of the test statistic is greater than the absolute value of the critical value, reject the null hypothesis.
- If the p-value is less than the level of significance (0.05), reject the null hypothesis.
What does this mean?
- If we reject the null hypothesis, it means that there is evidence to support the alternative hypothesis, suggesting that there is a significant difference between the means of the two samples.
- If we do not reject the null hypothesis, it means that there is not enough evidence to support the alternative hypothesis, indicating that there is no significant difference between the means of the two samples.