7.76 New hybrid tablet and laptop? The purchasing department has suggested your company switch to a new hybrid tablet and laptop. As CEO, you want data to be assured that employees will like these new hybrids over the old laptops. You designate the next 16 employees needing a new laptop to participate in an experiment in which eight will be randomly assigned to receive the standard laptop and the remainder will receive the new hybrid tablet and laptop. After a month of use, these employees will express their satisfaction with their new computers by responding to the statement “I like my new computer” on a scale from 1 to 5, where 1 represents “strongly disagree,” 2 is “disagree,” 3 is “neutral,” 4 is “agree,” and 5 is “strongly agree.”
(a) The employees with the hybrid computers have an average satisfaction score of 4.3 with standard deviation 0.7. The employees with the standard laptops have an average of 3.7 with standard deviation 1.5. Give a 95% confidence interval for the difference in the mean satisfaction scores for all employees.
(b) Would you reject the null hypothesis that the mean satisfaction for the two types of computers is the same versus the two-sided alternative at significance level 0.05? Use your confidence interval to answer this question. Explain why you do not need to calculate the test statistic.