Comparing Two Random Samples

A US market researcher was curious if there was a difference in electric vehicle ownership rates between people living on the East coast versus those on West coast. They obtained separate random samples of 500 car owners from each region. They found that 52 in the West coast sample owned an electric car compared to 38 in the East coast sample. They plan to use these results to do a two-sample z test to see if these results show a significant difference.

Which conditions for this type of test did their samples meet?

• Both samples were randomly selected from their populations.

• The expected counts of successes and failures are sufficiently large in each sample.

• Individual observations in each sample can be considered independent, and the samples themselves are independent.

For a simple random sample of 100 cars of a certain popular model in 20012, it was found that 20 had a certain minor defect in the brakes. For an independent SRS of 400 cars of the same model in 2009, it was found that 50 had the same defect. Let p₁ and p₂ be the proportions of all cars of this model in 2012 and 2009, respectively, that have the defect. A 90% confidence interval for p₁ – p₂ is (approximately)

• 0.075 ± 0.085

• 0.075 ± 0.071

• 0.075 ± 0.043

The following table gives the percent of fat found in 5 randomly selected containers of each of two brands of ice cream.
Brand A   5.7   4.5   6.2   6.3   7.3
Brand B   6.3   5.7   5.9   6.4   5.1
If you wanted to estimate the difference in mean fat content, which of the following procedures is appropriate?

• Paired t interval

• Paired t test

• Two-sample t interval

• Two-sample t test

• Two-sample z interval

• Both dotplots are roughly symmetric. There are no outliers in either dotplot.

• Both dotplots are roughly symmetric. The dotplot of sample 2 has an outlier.

• Both dotplots are strongly skewed to the right. There are no outliers in either dotplot.

• Both dotplots are roughly symmetric. Both dotplots have one upper outlier.

• t procedures are not recommended in any of these cases.

Different varieties of fruits and vegetables have different amounts of nutrients. These differences are important when these products are used to make baby food. We wish to compare the mean carbohydrate content of two varieties of peaches. We wish to test if the two varieties are significantly different in their mean carbohydrate content. Which of the following are the appropriate null and alternative hypotheses for this situation?

• 28±0.148

• 0.25±0.057

• 0.25±0.094

• 0.25±0.112

• 0.25±0.148