Homework Help is Here – Start Your Trial Now!
Math
Statistics
Ages of Gamblers The mean age of a sample of 22 people who were playing the slot machines is 49.3 years, and the standard deviation is 6.8 years. The mean age of a sample of 31 people who were playing roulette is 54.3 with a standard deviation of 3.2 years. Can it be concluded at a = 0.05 that the mean age of those playing the slot machines is less than those playing roulette? Use u, for the mean age of those playing slot machines. Assume the variables are normally distributed and the variances are unequal. Part: 0 / 5 Part 1 of 5 State the hypotheses and identify the claim with the correct hypothesis. Ho : (Choose one) ▼ H : (Choose one) ▼ This hypothesis test is a (Choose one) ▼ test.

Ages of Gamblers The mean age of a sample of 22 people who were playing the slot machines is 49.3 years, and the standard deviation is 6.8 years. The mean age of a sample of 31 people who were playing roulette is 54.3 with a standard deviation of 3.2 years. Can it be concluded at a = 0.05 that the mean age of those playing the slot machines is less than those playing roulette? Use u, for the mean age of those playing slot machines. Assume the variables are normally distributed and the variances are unequal. Part: 0 / 5 Part 1 of 5 State the hypotheses and identify the claim with the correct hypothesis. Ho : (Choose one) ▼ H : (Choose one) ▼ This hypothesis test is a (Choose one) ▼ test.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
See similar textbooks
icon
Related questions
Question
The first pic is the question. Since some tutors have been solving the problems wrong recently (no judgment), I’ve added a sample question to solve problem.
Ages of Gamblers The mean age of a sample of 22 people who were playing the slot machines is 49.3 years, and the standard deviation is 6.8 years. The mean age of a sample of 31 people who were playing roulette is 54.3 with a standard deviation of 3.2 years. Can it be concluded at a= 0.05 that the mean age of those playing the slot machines is less than those playing roulette? Use u, for the mean age of those playing slot machines. Assume the variables are normally distributed and the variances are unequal. Part: 0 / 5 Part 1 of 5 State the hypotheses and identify the claim with the correct hypothesis. Ho : (Choose one) H : (Choose one) ▼ This hypothesis test is a (Choose one) ▼ test.
Transcribed Image Text:Ages of Gamblers The mean age of a sample of 22 people who were playing the slot machines is 49.3 years, and the standard deviation is 6.8 years. The mean age of a sample of 31 people who were playing roulette is 54.3 with a standard deviation of 3.2 years. Can it be concluded at a= 0.05 that the mean age of those playing the slot machines is less than those playing roulette? Use u, for the mean age of those playing slot machines. Assume the variables are normally distributed and the variances are unequal. Part: 0 / 5 Part 1 of 5 State the hypotheses and identify the claim with the correct hypothesis. Ho : (Choose one) H : (Choose one) ▼ This hypothesis test is a (Choose one) ▼ test.
Sample Question Ages of Gamblers The mean age of a sample of 21 people who were playing the slot machines is 48.1 years, and the standard deviation is 6.8 years. The mean age of a sample of 30 people who were playing roulette is 54.7 with a standard deviation of 3.2 years. Can it be concluded at a=0.05 that the mean age of those playing the slot machines is less than those playing roulette? Use u, for the mean age of those playing slot machines. Assume the variables are normally distributed and the variances are unequal. (a) State the hypotheses and identify the claim with the correct hypothesis. (b) Find the critical value(s). (c) Compute the test value. (d) Make the decision. (e) Summarize the results. Explanation (a) State the hypotheses and identify the claim with the correct hypothesis. The null hypothesis H, is the statement that there is no difference between the means. This is equivalent to u, = lz. The alternative hypothesis H is the statement that there is a difference between the means. In this case, the mean age of slot machine players is less than the mean age of roulette players. This is equivalent to u, <Hz. The problem asks if the "mean age of those playing the slot machines is less than those playing roulette." Hence, the claim is the alternative hypothesis II,. (b) Find the critical value(s). For this problem, n, = 21 and n,= 30. The degrees of freedom are the smaller of 21 -1= 20 or 30-1= 29. Hence, d.f. = 20. From OThe t Distribution Table, for a left-tailed test with a =0.05 and d.f. = 20, the critical value is - 1.725. (c) Compute the test value. Using the formula for the i test-for testing the difference between two means-independent samples, compute the test value: (*ri – In) - (*x – 'x) (48.1 – 54.7)-0 6.8 3.2 21 30 = -4.139 Hence, the test value rounded to 3 decimal places is t= -4.139. (d) Make the decision. Since the test value falls in the critical region, reject the null hypothesis. -4.139 -1.725 0 (e) Summarize the results. Since the null hypothesis was rejected, there is enough evidence to support the claim.
Transcribed Image Text:Sample Question Ages of Gamblers The mean age of a sample of 21 people who were playing the slot machines is 48.1 years, and the standard deviation is 6.8 years. The mean age of a sample of 30 people who were playing roulette is 54.7 with a standard deviation of 3.2 years. Can it be concluded at a=0.05 that the mean age of those playing the slot machines is less than those playing roulette? Use u, for the mean age of those playing slot machines. Assume the variables are normally distributed and the variances are unequal. (a) State the hypotheses and identify the claim with the correct hypothesis. (b) Find the critical value(s). (c) Compute the test value. (d) Make the decision. (e) Summarize the results. Explanation (a) State the hypotheses and identify the claim with the correct hypothesis. The null hypothesis H, is the statement that there is no difference between the means. This is equivalent to u, = lz. The alternative hypothesis H is the statement that there is a difference between the means. In this case, the mean age of slot machine players is less than the mean age of roulette players. This is equivalent to u, <Hz. The problem asks if the "mean age of those playing the slot machines is less than those playing roulette." Hence, the claim is the alternative hypothesis II,. (b) Find the critical value(s). For this problem, n, = 21 and n,= 30. The degrees of freedom are the smaller of 21 -1= 20 or 30-1= 29. Hence, d.f. = 20. From OThe t Distribution Table, for a left-tailed test with a =0.05 and d.f. = 20, the critical value is - 1.725. (c) Compute the test value. Using the formula for the i test-for testing the difference between two means-independent samples, compute the test value: (*ri – In) - (*x – 'x) (48.1 – 54.7)-0 6.8 3.2 21 30 = -4.139 Hence, the test value rounded to 3 decimal places is t= -4.139. (d) Make the decision. Since the test value falls in the critical region, reject the null hypothesis. -4.139 -1.725 0 (e) Summarize the results. Since the null hypothesis was rejected, there is enough evidence to support the claim.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
SEE MORE TEXTBOOKS