Question

Consider each of the scenarios below. For each statement, decide which statistical procedure is most appropriate.

1. Mr. Taylor's 4th grade class uses Skittles to learn about probability. They open several randomly selected bags of Skittles and sort and count the different colors and want to determine if Skittles are evenly distributed by color.

2. An insurance company selected a random sample of 500 clients under 18 years of age and found that 180 of them had had an accident in the previous year. A random sample of 600 clients aged 18 and older was also selected and 150 of them had had an accident in the past year. We want to determine how much the accident proportions differ between the two age groups.

3. The manufacturer of an over-the-counter heartburn relief mediation claims that it product brings relief in less than 3.5 minutes, on average. To be able to make this claim the manufacturer was required by the FDA to present statistical evidence in support of the claim. The manufacturer reported that for a sample of 50 heartburn sufferers, the mean time to relief was 3.3 minutes and the standard deviation was 1.1 minutes.

4. A nutritionist wants to know the proportion of Americans who say they limit their consumption of artificial sweeteners. A poll of 2537 US adults is conducted and the proportion is recorded.

5. The dean of the College of Natural Science want to know if undergraduate students from the statistics department perform better, the same as, or worse than students from the math department on the quantitative portion of the GRE (Graduate Record Examinations). They take a sample of students from each department who have taken the GRE and compare scores.

Answer 1

1. Chi-square for goodness of fit.

2. Two-sample proportion test

3. One-sample hypothesis test for mean

4. One-sample proportion test

5. Two-sample hypothesis test for mean

Explanation:

The statistical procedures suitable for each of these scenarios.

1) Chi-square for goodness of fit

In Chi-Square goodness of fit test, the term goodness of fit is used to compare the observed sample distribution with the expected probability distribution. Chi-Square goodness of fit test determines how well theoretical distribution fits the empirical distribution. In Mr Taylor's class' observation, the expected sample distribution is even distribution, by counting and sorting, they want to determine the theoretical distribution. Therefore Chi-square for goodness of fit is suitable.

2) Two - sample proportion test

Two sample proportion test is used to determine whether the proportions of two groups differ. It calculates the range of values that is likely to include the difference between the population proportions. Since there are two groups and we want to determine the proportion at which they differ, two-sample proportion test is suitable.

3) One - sample hypothesis test for mean

The One Sample Test is commonly used to test the Statistical difference between a sample mean and a known value of the mean in the population.

4) One-sample proportion test

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value. The only population here is the population of Americans claiming to limit their consumption of sweeteners.

5) Two-sample hypothesis test for mean

The two-sample hypothesis test is used to determine if two population means are equal. The two populations here are the undergraduate students from the statistics department and the math department.

Answer 2

1. Chi-square test for multiple categories of a single variable

2. Two-sample hypothesis test for the difference in proportions

3. One-sample confidence interval for a single mean

4. Two-sample hypothesis test for the difference in means

5. One-sample hypothesis test for a single mean