Question

A random sample of 15 students showed that their average fear of math was 84.8 on...

A random sample of 15 students showed that their average fear of math was 84.8 on a 1-100 scale, with a standard deviation of 2.7. At the α = .01 significance level, test the claim that the average fear of math of all students is below 85 on this scale. b) Suppose now the same mean and standard deviation were found in a random sample of 10000 students. Again, at the α = .01 significance level, test the claim that the average fear of math of all students is below 85.

Homework Answers

Answer #1

a) As we are testing here whether the mean is below 85, therefore the test statistic here is computed as:

For n - 1 = 14 degrees of freedom, as this is a one tailed test, the p-value is obtained from the t distribution tables as:
p = P( t14 < -0.2869) = 0.3892

As the p-value here is 0.3892 > 0.01, therefore the test is not significant and we dont have sufficient evidence here that population mean is below 85 here.

b) For n = 10,000 the test statistic here is computed as:

For 10000 - 1 = 9999 degrees of freedom, the p-value here is obtained from the t distribution tables as 0 because the test statistic magnitude is very high. Therefore the test is significant here and we can reject the null hypothesis and conclude that we have sufficient evidence that the population mean is less than 85 here.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A random sample of 20 students at a university showed an average age of 20.9 years...
A random sample of 20 students at a university showed an average age of 20.9 years and a sample standard deviation of 2.5 years. The 98% confidence interval for the true average age of all students in the university is? Enter in the upper limit of your confidence interval.
A random sample of 20 students at a university showed an average age of 21.5 years...
A random sample of 20 students at a university showed an average age of 21.5 years and a sample standard deviation of 2.8 years. The 98% confidence interval for the true average age of all students in the university is? Enter in the upper limit of your confidence interval. ( round to 4 decimal places)
A community college Math instructor feels that the average number of units students enroll in each...
A community college Math instructor feels that the average number of units students enroll in each semester has increased since he was a student at community college. Looking up data from the year the instructor started teaching, the mean number of units community college students enrolled was 14.3 units, with a population standard deviation of 3.2 units. The Math instructor took a sample of 40 of the current community college students and found that the sample had a mean number...
. A certain test preparation course is designed to improve students' SAT Math scores. The students...
. A certain test preparation course is designed to improve students' SAT Math scores. The students who took the prep course have a mean SAT Math score of 504 with a standard deviation of 38.5, while the students who did not take the prep course have a mean SAT Math score of 492 with a standard deviation of 43.5. The SAT Math scores are taken for a sample of 78 students who took the prep course and a sample of...
A community college Math instructor feels that the average age of community college students decreased since...
A community college Math instructor feels that the average age of community college students decreased since they started teaching 25 years ago. Looking up data from the year the instructor started teaching, the mean age of community college students was 24.3 years old, with a population standard deviation of 2.2 years. The Math instructor took a sample of 40 of their current community college students and found that the sample had a mean age of 23.7 years old. Assume the...
For all U.S. students nationally who take the SAT, the average SAT Math score is 500,...
For all U.S. students nationally who take the SAT, the average SAT Math score is 500, with a population standard deviation of 125. A random sample of 10 students entering Whitmer College had an average SAT Math (SAT-M) score of 530. The sample data can be used to test the claim that the mean SAT-M score of all Whitmer College students is different than the national mean SAT-M score. Based on the given information, have the conditions for this hypothesis...
Math SAT: The math SAT test was originally designed to have a mean of 500 and...
Math SAT: The math SAT test was originally designed to have a mean of 500 and a standard deviation of 100. The mean math SAT score last year was 515 but the standard deviation was not reported. You read in an article for an SAT prep course that states in a sample of 87 students, the mean math score was 534, but they did not disclose the standard deviation. Assume the population standard deviation (σ) for all prep course students...
Five years ago, the average math SAT score for students at one school was 475. A...
Five years ago, the average math SAT score for students at one school was 475. A teacher wants to perform a hypothesis test to determine whether the mean math SAT score of students at the school has improved. The mean math SAT score for a random sample of 40 students from this school is 469 with a standard deviation of 73. Do the data provide sufficient evidence to conclude that the mean math SAT score for students at the school...
Q1) A random sample of 10 travel brochures showed sample mean cost of an 8-day cruise...
Q1) A random sample of 10 travel brochures showed sample mean cost of an 8-day cruise to the Bahamas $1,978. (1st class, double occupancy). The sample standard deviation was $250. An independent random sample of 12 travel brochures showed mean cost of a comparable 8 day cruise to Mexico $2,150 with sample standard deviation $275. Test to see if the population mean costs for the two types of cruises are different. Use a 1% significance level. Step 1: Ho: Ha:...
For all U.S. students nationally who take the SAT, SAT Math scores are normally distributed with...
For all U.S. students nationally who take the SAT, SAT Math scores are normally distributed with an average score of 500 for all U.S. students and a population standard deviation of 125. A random sample of 100 students entering Whitmer College had an average SAT Math (SAT-M) score of 530. The sample data can be used to test the claim that the mean SAT-M score of all Whitmer College students is different than the national mean SAT-M score. From the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT