Question

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

  ?    One-sample hypothesis test for a single proportion    One-sample confidence interval for a single proportion    Two-sample hypothesis test for the difference in proportions    Two-sample confidence interval for the difference in proportions    Chi-square test for multiple categories of a single variable    Chi-square test of independence of 2 categorical variables    One-sample hypothesis test for a single mean    One-sample confidence interval for a single mean    Two-sample hypothesis test for the difference in means    Two-sample confidence interval for the difference in means      1. 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 if the accident proportions differ between the two age groups.

  ?    One-sample hypothesis test for a single proportion    One-sample confidence interval for a single proportion    Two-sample hypothesis test for the difference in proportions    Two-sample confidence interval for the difference in proportions    Chi-square test for multiple categories of a single variable    Chi-square test of independence of 2 categorical variables    One-sample hypothesis test for a single mean    One-sample confidence interval for a single mean    Two-sample hypothesis test for the difference in means    Two-sample confidence interval for the difference in means      2. 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.

  ?    One-sample hypothesis test for a single proportion    One-sample confidence interval for a single proportion    Two-sample hypothesis test for the difference in proportions    Two-sample confidence interval for the difference in proportions    Chi-square test for multiple categories of a single variable    Chi-square test of independence of 2 categorical variables    One-sample hypothesis test for a single mean    One-sample confidence interval for a single mean    Two-sample hypothesis test for the difference in means    Two-sample confidence interval for the difference in means      3. A claim is made that 87% of college undergraduates send more than 10 text messages per day. You collect a random sample of undergraduates to determine if the claim is reasonable or not.

  ?    One-sample hypothesis test for a single proportion    One-sample confidence interval for a single proportion    Two-sample hypothesis test for the difference in proportions    Two-sample confidence interval for the difference in proportions    Chi-square test for multiple categories of a single variable    Chi-square test of independence of 2 categorical variables    One-sample hypothesis test for a single mean    One-sample confidence interval for a single mean    Two-sample hypothesis test for the difference in means    Two-sample confidence interval for the difference in means      4. A researcher wants to estimate the average yearly cost of attendance at community colleges in the US. They collect a simple random sample of 50 community colleges and calculate the mean and sd of the yearly cost of attendance at each school.

  ?    One-sample hypothesis test for a single proportion    One-sample confidence interval for a single proportion    Two-sample hypothesis test for the difference in proportions    Two-sample confidence interval for the difference in proportions    Chi-square test for multiple categories of a single variable    Chi-square test of independence of 2 categorical variables    One-sample hypothesis test for a single mean    One-sample confidence interval for a single mean    Two-sample hypothesis test for the difference in means    Two-sample confidence interval for the difference in means      5. 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.

Answer 1

1. Given 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 if the accident proportions differ between the two age groups.

In such situation we used Two-sample hypothesis test for the difference in proportions.

Since we have to test whether there is a difference of proportions in the two age groups.

2. Given 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.

In such situation we used One-sample hypothesis test for a single proportion. Since we want to test the single population proportion.

3. A claim is made that 87% of college undergraduates send more than 10 text messages per day. You collect a random sample of undergraduates to determine if the claim is reasonable or not.

In such situation we used One-sample hypothesis test for a single proportion. Since we want to test the single population proportion.

4. A researcher wants to estimate the average yearly cost of attendance at community colleges in the US. They collect a simple random sample of 50 community colleges and calculate the mean and sd of the yearly cost of attendance at each school.

In such situation we used One-sample hypothesis test for a single mean. Since population standard deviation is not known we used t test for testing the significance of the population mean.

5. 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.

In such situation we used Two-sample hypothesis test for the difference in proportions.

Since we have to test whether there is a difference of proportions in the two age groups.