# Designs for comparing means us

Designs for comparing means using College Board data on SATscores. Please write the null and alternative hypotheses such thatit is clear we are testing which of the following: 1) a single meanversus a claim in null hypothesis, 2) Means from two independentsamples, or 3) Means from matched pairs. Also state the degrees offreedom associated with the t-test. (2 points for correcthypotheses, 1 point for df)

a.) The college board aims to achieve a mean of 500 on the Mathsection of the SAT each year. A researcher randomly selects 50 MathSAT scores from Fort Collins college-bound seniors to see if theFort Collins mean is different than 500.

b.) A researcher randomly selects 23 male Math SAT scores and 29female Math SAT scores from Fort Collins college-bound seniors tosee if their means are different.

c.) A researcher randomly selects 26 Math SAT scores from oneFort Collins high-school and 21 scores from another Fort Collinshigh-school and tests for a difference between means.

d.) A researcher randomly selects 25 SAT scores and tests for adifference between the mean of the Math SAT and the mean of theCritical Reading SAT score.

e.) A researcher randomly selects 20 high-schools acrossColorado and then randomly selects 2 male Math SAT scores from eachschool to test for a difference in the overall mean with thenational average for males.

Solution;-

a)

Test

State the hypotheses. The first step is tostate the null hypothesis and an alternative hypothesis.

Null hypothesis: u = 500Alternative hypothesis: u 500(Claim)

Note that these hypotheses constitute a two-tailed test.

D.F = n – 1

D.F = 49

b)

State the hypotheses. The first step is tostate the null hypothesis and an alternative hypothesis.

Null hypothesis: u1 = u 2Alternative hypothesis: u1u 2 (Claim)

Note that these hypotheses constitute a two-tailed test.

D.F = n1 + n2 – 2

D.F = 23 + 29 – 2

D.F = 50

c)

State the hypotheses. The first step is tostate the null hypothesis and an alternative hypothesis.

Null hypothesis: u1 = u 2Alternative hypothesis: u1u 2

Note that these hypotheses constitute a two-tailed test.

D.F = n1 + n2 – 2

D.F = 26 + 21 – 2

D.F = 45

d) matched pair test

State the hypotheses. The first step is tostate the null hypothesis and an alternative hypothesis.

Null hypothesis: ud = 0

Alternative hypothesis: ud ≠ 0

Note that these hypotheses constitute a two-tailed test.

D.F = n – 1

D.F = 25 – 1

D.F = 24

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