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Day 1 Testing Paired Differences (independent samples)

Comparing period 5 Calc average on the midterm and period 6 Calc average midterm?

Get a random sample of seniors and compare GPAs of girls to GPA of boys… If the samples are independent then you compare mean differences using a new formula

1 1 1 1 2 2 2 2 0 μ 1 0 μ 1 0 μ 1 0 μ 1 μ μ 2 μ 2 μ 2 2 Left Tailed Right Tailed Two Tailed Customary…

x 1 and x 2 should have normal distributions with mean μ 1 and μ 2 . If both n 1 and n 2 are larger than 30, then the CLT assures you that the distributions of the xbars are normal.

So glad you asked!! Using the same pattern 1. State null and alternate hypotheses 2. Compute your test statistic 3. Find the P-value that corresponds to the sample test statistic 4. Conclude 5. State your conclusion

z x 1 x 2 z σ 1 2 n 1 x 1 σ 2 2 n 2 x 2 σ 1 2 n 1 σ 2 2 n 2 2

t x 1 x 2 t s 1 2 n 1 x 1 s 2 2 n 2 x 2 s 1 2 n 1 s 2 2 n 2 2

A random sample of n 1 =12 winter days in For Englewood (a suburb of Denver) a random sample of n 2 =14 winter days gave a pollution index is normally distributed, and previous studies show σ 1 = 21 and σ 2 = 15.

Does this information suggest that the mean population pollution index of Englewood is different from Denver in the winter?

Use 1% level of significance.

A random sample of n 1 =16 communities in western Kansas gave an average rate of hay fever (per 1000, under 25 yrs of age) of 109.50 with a sample standard deviation of 15.41. A random sample of n 2 =14 regions in western Kansas gave an average rate of hay fever (per 1000, over 50 yrs of age) of 99.36 with a sample standard deviation of 11.57.

Assuming that the hay fever rate of each group is approximately normal, does the data suggest that the 50+ has a lower rate of hay fever?

Use a 5% level of confidence.