The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's in-state and out-of-state applicants. A random sample of 8 in-state applicants results in a SAT scoring mean of 1144 with a standard deviation of 25. A random sample of 17 out-of-state applicants results in a SAT scoring mean of 1200 with a standard deviation of 26. Using this data, find the 90% confidence interval for the true mean difference between the scoring mean for in-state applicants and out-of-state applicants. Assume that the population variances are not equal and that the two populations are normally distributed. Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean score of in-state applicants

x2 = sample mean score of out-of-state applicants

s1 = sample standard deviation for in-state applicants

s2 = sample standard deviation for out-of-state applicants

n1 = number of in-state applicants

n2 = number of out-of-state applicants

For a 90% confidence interval, we would determine the z score from the t distribution table because the number of samples are small

Degree of freedom =

(n1 - 1) + (n2 - 1) = (8 - 1) + (17 - 1) = 23

z = 1.714

x1 - x2 = 1144 - 1200 = - 56

Margin of error = z√(s1²/n1 + s2²/n2) = 1.714√(25²/8 + 26²/17) = 18.61

Confidence interval = - 56 ± 18.61

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for