Question

3 2) At the Kinglet School District, the average score over the past 5 years for the math portion of the Scholastic Aptitude Test (SAT) was 411. An educator believes that recent changes to the state math curriculum has resulted in increased scoring on this part of the test. In an attempt to verify this, she gathers a SRS of 14 students and has them take the math portion of the SAT with the following results (assume the population of SAT scores is normally distributed). Please use data table and your ID letter for your data. 440 410 410 400 430 450 450 440 400 440 390 440 410 410 Does this evidence appear to support the educator's claim that the population scores have increased at her school at the 5% significance level? (Circle either Yes or No). 1214 YES NO X=422.86 Please show the four steps of your analysis in the space provided below... 8-20.54 Hom= 411 Haigus 411

Please help with all steps.

Answer 1

$\\\mu_0 = 411 \\n = 14 \\s = 20.54 \\\bar{X} = 422.86 \\\alpha = 0.05$

The test hypothesis is

$\\\text{Null Hypothesis }--> H_0: \mu = \mu_0 \\\text{Alternate Hypothesis }--> H_1: \mu > \mu_0$

This is a right-tailed test because the alternative hypothesis is formulated to detect claim if difference of data is more than 0.

Now, the value of test static can be found out by following formula:

X - μo to s/n 422.86 – 411.0 to 20.54/14 to = 2.1605 Critical value = ta,n-1 to.05,13 = 1.7709 Rejection Region: to > tan-1 Since to 2.1605 > 1.7709 t0.05, we reject the null hypothesis Ho : 411.0 in favor of the alternative hypothesis H1 :u > 411.0 at a = 0.05.

Yes

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