##### Question

In: Statistics and Probability

# A student researcher compares the heights of American students and non-American students from the student body...

A student researcher compares the heights of American students and non-American students from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 1818 American students had a mean height of 68.968.9 inches with a standard deviation of 2.712.71 inches. A random sample of 1212 non-American students had a mean height of 65.765.7 inches with a standard deviation of 2.172.17 inches. Determine the 90%90% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 3: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 3: Find the standard error of the sampling distribution to be used in constructing the confidence interval. Round your answer to two decimal places.

Step 3 of 3: Construct the 90%90% confidence interval. Round your answers to two decimal places.

## Solutions

##### Expert Solution

Solution :

Step 1 of 3 : Critical value t = 1.701

Step 2 of 3 : Standard error Se = 0.94 (rounded)

Step 3 of 3 : The 90% confidence interval is (1.61,4.79) (rounded)

Explanation :-

Given that, for American students : X1-bar = 68.9 , s1 = 2.71 , n = 18

for Non-American students : X2-bar = 65.7 , s1 = 2.17 , n = 12 ## Related Solutions

##### A student researcher compares the heights of American students and non-American students from the student body...
A student researcher compares the heights of American students and non-American students from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 12 American students had a mean height of 67.7 inches with a standard deviation of 3.06 inches. A random sample of 17 non-American students had a mean height of 64.7 inches with a standard deviation of 1.97inches. Determine the 90% confidence interval for the true mean...
##### A student researcher compares the heights of American students and non-American students from the student body...
A student researcher compares the heights of American students and non-American students from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 17 American students had a mean height of 70 inches with a standard deviation of 1.73 inches. A random sample of 12 non-American students had a mean height of 66 inches with a standard deviation of 2.23 inches. Determine the 90% confidence interval for the true...
##### A student researcher compares the heights of men and women from the student body of a...
A student researcher compares the heights of men and women from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 10 men had a mean height of 71.3 inches with a standard deviation of 2.34 inches. A random sample of 17 women had a mean height of 65.5 inches with a standard deviation of 2.72 inches. Determine the 98% confidence interval for the true mean difference between the...
#####  Sixty percent of the student body at the University of British Columbia is from British...
 Sixty percent of the student body at the University of British Columbia is from British Columbia, 30% percent are from other Canadian provinces and territories, and the remainder are international students. Twenty percent of students from British Columbia live in the dormitories, whereas 50% of students from other Canadian provinces and territories live in the dormitories. Finally, 80% of the international students live in the dormitories. What percentage of University of British Columbia students live in the dormitories? Given...
##### A researcher is interested in heart rates of university students. The researcher randomly selects 52 students...
A researcher is interested in heart rates of university students. The researcher randomly selects 52 students from a class they are teaching and measures the students’ heart rates. The data obtained is in the file “Heart Rates.csv”. 1. What is the target population? What is the study population? What is an individual? 2. Is this an observational study or an experiment? 3. The tools you have learned for doing statistical inference require that certain assumptions be met. Check whether these...
##### A researcher compares the effectiveness of two different instructional methods for teaching physiology. A sample of...
A researcher compares the effectiveness of two different instructional methods for teaching physiology. A sample of 54 students using Method 1 produces a testing average of 51.7. A sample of 90 students using Method 2 produces a testing average of 56.8. Assume that the population standard deviation for Method 1 is 7.35, while the population standard deviation for Method 2 is 16.72. Determine the 80% confidence interval for the true difference between testing averages for students using Method 1 and...
##### A researcher compares the effectiveness of two different instructional methods for teaching physiology. A sample of...
A researcher compares the effectiveness of two different instructional methods for teaching physiology. A sample of 214 students using Method 1 produces a testing average of 53.9. A sample of 193 students using Method 2 produces a testing average of 88.9. Assume that the population standard deviation for Method 1 is 17.61, while the population standard deviation for Method 2 is 11.73. Determine the 99% confidence interval for the true difference between testing averages for students using Method 1 and...
##### A researcher compares two compounds (1 and 2) used in the manufacture of car tires that...
A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. SUVs equipped with tires using compound 1 have a mean braking distance of 62 feet and a standard deviation of 10.6 feet. SUVs equipped with tires using compound 2 have a mean braking distance of 68 feet and a standard deviation of 13.9 feet. Suppose that a sample of 77 braking tests...
##### A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of...
A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 215215 students using Method 1 produces a testing average of 55.555.5. A sample of 242242 students using Method 2 produces a testing average of 64.264.2. Assume that the population standard deviation for Method 1 is 7.957.95, while the population standard deviation for Method 2 is 18.2118.21. Determine the 90%90% confidence interval for the true difference between testing averages for students using Method 1 and...
##### A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of...
A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 61 students using Method 1 produces a testing average of 88.6A sample of 111111 students using Method 2 produces a testing average of 64.9 Assume that the population standard deviation for Method 1 is 14.68, while the population standard deviation for Method 2 is 5.52. Determine the 90%90%confidence interval for the true difference between testing averages for students using Method 1 and students using...