Question

1. A random sample of 13 fields of durum wheat has a mean yield of 28.3 bushels per acre and standard deviation of 4.28 bushels per acre. Determine the 98% confidence interval for the true mean yield. Assume the population is approximately normal.

1. Identify the parameter we are estimating using words or the proper statistical symbol. (1 point)
2. Check the conditions that would allow us to construct and interpret this CI. (1 point)
3. Interpret the CI in the context of the problem. (1 point)

2. The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's in-state and out-of-state applicants. A random sample of 9 in-state applicants results in a SAT scoring mean of 1231 with a standard deviation of 36. A random sample of 19 out-of-state applicants results in a SAT scoring mean of 1161 with a standard deviation of 37. Using this data, find the 98% confidence interval for the true mean difference between the scoring mean for in-state applicants and out-of-state applicants. Assume that the population variances are not equal and that the two populations are normally distributed.

1. Identify the parameter we are estimating using words or the proper statistical symbol. (1 point)
2. Check the conditions that would allow us to construct and interpret this CI. (1 point)
3. Interpret the CI in the context of the problem. (1 point)

3. An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. Suppose that the mean income is found to be $22.1 for a random sample of 987 people. Assume the population standard deviation is known to be $6.9. Construct the 90% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.

1. Identify the parameter we are estimating using words or the proper statistical symbol. (1 point)
2. Check the conditions that would allow us to construct and interpret this CI. (1 point)
3. Interpret the CI in the context of the problem. (1 point)

4. The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level.

Step 2 of 2:

Suppose a sample of 2339 tenth graders is drawn. Of the students sampled, 1942 read above the eighth grade level. Using the data, construct the 99% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.

1. Identify the parameter we are estimating using words or the proper statistical symbol. (1 point)
2. Check the conditions that would allow us to construct and interpret this CI. (1 point)
3. Interpret the CI in the context of the problem. (1 point)

Answer 1