Section 11.3 – Inference About Two Means: Independent Samples

Objectives

  1. Test hypotheses regarding the difference of two independent means
  2. Construct and interpret confidence intervals regarding the difference of two independent means

Objective 1 – Test hypotheses regarding the difference of two independent means

Example

Given the sample data below (assume that the populations are normally distributed)

Population 1 / Population 2
n / 20 / 20
/ 111 / 104
s / 8.6 / 9.2

Test whether 12 at the  = 0.05 level of significance. Either Reject H0 or Do Not Reject H0

Example

Given the sample data below (assume that the populations are normally distributed)

Population 1 / Population 2
n / 40 / 32
/ 94.2 / 115.2
s / 15.9 / 23.0

Test whether 12 at the  = 0.05 level of significance. Either Reject H0 or Do Not Reject H0

Example

A researcher wanted to know whether “state” quarters had a weight that is more than “traditional” quarters. He randomly selected 18 “state” quarters and 16 “traditional” quarters, weighed each of them and obtained the following data.

Test the claim that “state” quarters have a mean weight that is more than “traditional” quarters at the α = 0.05 level of significance.

NOTE: A normal probability plot of “state” quarters indicates the population could be normal. A normal probability plot of “traditional” quarters indicates the population could be normal

Example

For a sample of 1,657 men (ages 65-74), the mean weight is 164 lbs and the standard deviation is 27 lbs. For a sample of 804 men (ages 25-34), the mean weight is 176 lbs and the standard deviation is 35 lbs. Test the claim that the older men come from a population with a mean weight that is less than the mean weight for men in the younger age bracket. Use α = 0.01.

Example

A study of zinc-deficient mothers was conducted to determine whether zincsupplementation during pregnancy results in babies with increased weights at birth. Is there sufficient evidence at α = 0.05 to support the claim that zinc supplementation does result in increased birth weight?

(weights measured in grams)Zinc SupplementPlacebo

n1 = 294n2 = 286

= 3214 = 3088

s1 = 669s2 = 728

Objective 2 - Construct and interpret confidence intervals regarding the difference of two independent means

Given the sample data below (assume that the populations are normally distributed)

Population 1 / Population 2
n / 20 / 20
/ 111 / 104
s / 8.6 / 9.2

Construct a 95% confidence interval about 1 - 2 .

Example

Given the sample data below (assume that the populations are normally distributed)

Population 1 / Population 2
n / 40 / 32
/ 94.2 / 115.2
s / 15.9 / 23.0

Construct a 95% confidence interval about 1 - 2 .

Example

Construct a 95% confidence interval about the difference between the population mean weight of a “state” quarter versus the population mean weight of a “traditional” quarter (continued from example in objective 1).

Example

In a Gallup poll conducted August 32-September 2, 2009, 513 national adults aged 18 years of age or older who consider themselves to be Republican were asked “Of every tax dollar that goes to the federal government in Washington, DC, how many cents of each dollar are would you say are wasted?” The mean was found to be 54 cents with a standard deviation of 2.9 cents. The same question was asked of 513 Democrats. The mean was 41 cents with a standard deviation of 2.6 cents. Construct a 95% confidence interval for the mean difference in government waste, R - D and interpret the interval.

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