Z-test for Means Formulas



Independent Samples t-test HW

Recall the following problem from lab:

In an attempt to show that the Graduate Record Exam is generally biased against Hispanics, a psychologist obtains quantitative GRE scores (range 100 to 800) of 16 Caucasians and 9 Hispanics from the same college. The 25 individuals have similar social economic backgrounds and educational histories. The data follow:

Caucasian: 550, 500, 600, 650, 500, 625, 575, 590, 610, 580, 550, 610, 650, 590, 550, 560

Hispanics: 350, 700, 410, 500, 740, 380, 400, 690, 300

Is there a statistically significant difference between the two group means?

Work this problem out by hand using the formulas on the back of this sheet. Follow the steps in NHST as we have for the past few weeks in class. The only twist here is that you’ll need to compute the pooled variance for the t-test (see the formula) based on the sample variances.

You can begin by entering the data for each group into your calculator and filling in the table of descriptive statistics below.

Table of Descriptive Statistics

|Caucasian |Hispanics |

|n1 = 16 |n2 = 9 |

|01 = |02 = |

|s1 = |s2 = |

|[pic]= |[pic]= |

You can also check your results against those from SPSS.

Independent samples t-test Formulas

(to be used when you assume equal population variances)

Observed t-value

[pic] (this is referred to as the “pooled variance”)

[pic] ; df = n1 + n2 - 2

Effect size

[pic] Cohen’s: .2 small, .5 med., .8 lg

[pic] Cohen’s: .01 small, .06 med., .14 lg

Confidence Interval

[pic]

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