Question

Your beat submisnion for each entire question is used for your score O-13 points 0/2 Submissions Used My Notes Ask Your Teache Application Exercise: Idaho in the U.S. hired an education firm to implement a program to help students in science, technology, engineering, and math (STEM). The following year, the average math SAT portion of a sample of 580 students in Idaho was 515. The national math SAT average is 498 with a standard deviation of 97. State legislators are curious about the impact of the program. What can the legislators conclude with an a of 0.057 a) What is the appropriate test statistic? Select b) Population: Select Sample: Select c) Compute the appropriate test statistits) to make a decision about Ho (Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.) test statistic critical value Decision: Select d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below e) Compute the corresponding effect size(s) and indicate magnitude(s). If not appropriate, input and select "na" below Select Select f) Make an interpretation based on the results. Students from Idaho had significantly higher math SAT scores than the nation O Students from Idaho had significantly lower math SAT scores than the nation. O Students from Idaho did not have significantly different math SAT scores than the nation. Save Progress Submit Answer

Answer 1

a)
Since we know the population standard deviation, the appropriate test statistic is,
z test statistic

b)
Population - US Students
Sample - Sample of Idaho Students

c)
H0: $\mu$ = 498

H1: $\mu$ > 498

For $\alpha$ = 0.05, critical value of test statistic, z is 1.645

Standard error of mean = $\sigma$ /
n
= 97 /
LO
= 4.027706

Test statistic = (515 - 498) / 4.027706 = 4.22

Since the observed test statistic is greater than the critical value, Reject the null hypothesis

d)

Margin of error = Critical z * Std error = 1.645 * 4.027706 = 6.625576

95% CI of the true mean is,

(515 - 6.625576, 515 + 6.625576)

(508.3744,  521.6256)

e)

d = |x -$\mu$ |/ $\sigma$ = |515 - 498| / 97 = 0.1753

Since d is less than 0.2, the magnitude is small.

r² = na

f)

Students from Idaho had significantly higher math SAT scores than the nation.