Researchers investigated the speed with which consumers decide to purchase a pro

Question

Researchers investigated the speed with which consumers decide to purchase a product The researchers theorized that consumers with last names that begin with letters later in the alphabet will tend to acquire items faster than those whose last names begin with letters earlier m the alphabet-called the last name effect MBA students were offered tickets to a basketball game The first letter of the last name of respondents and their response times were noted The researchers compared the response times for two groups (1) those with last names beginning with a letter, A-J, and (2) those with last names beginning a letter, R-Z Summary statistics for the two groups are provided in the accompanying table Complete parts a and b below Click the icon to view the summary statistics. Construct a 90% confidence interval for the difference between the true mean response times for MBA students in the two groups The 90% confidence interval is (Round to two decimal places as needed )

Explanation / Answer

CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=22.57
Standard deviation( sd1 )=9.39
Sample Size(n1)=26
Mean(x2)=15.55
Standard deviation( sd2 )=8.68
Sample Size(n2)=26
CI = [ ( 22.57-15.55) ±t a/2 * Sqrt( 88.1721/26+75.3424/26)]
= [ (7.02) ± t a/2 * Sqrt( 6.29) ]
= [ (7.02) ± 1.708 * Sqrt( 6.29) ]
= [2.74 , 11.3]

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