Question

You took independent random samples of 20 students at City College and 25 students at SF State. You asked each student how many sodas they drank over the course of a year. The sample mean at City College was 80 and the sample standard deviation was 10. At State the sample mean was 90 and the sample standard deviation was 15. Use a subscript of c for City College and a subscript of s for State.

1. Calculate a point estimate of the difference between the two population means.

2. Calculate the appropriate number of degrees of freedom to use for your analysis. Hint: Remember that you always round down for degrees of freedom if you get a decimal answer. Note: To calculate this answer you must use the formula which assumes unequal variances.

3. Determine a 95% confidence interval for the difference between the two population means.

4. Give the null and alternative hypotheses for a hypothesis test to test to see if there is a statistically significant difference in the population means between students at the two schools.

5. State α using the confidence level in question 3.

6. Calculate the value of the test statistic.

7. Find a range for the p-value.

8. What is your conclusion in statistical terms?

9. Explain the meaning of this conclusion in business terms.

10. What statistical conclusion would you reach using the confidence interval approach? Explain how you reach this conclusion. Is it the same conclusion you reached using the p-value approach?

Answer 1

(10) Conclusion from confidence interval : Here, in given confidence interval zero lies outside the the confidence limits therefore we reject the null hypothesis.

And conclude that there is sufficient evidence to support the claim.

Conclusion from p value and confidence interval both are same.