Question

5. A random sample of 120 people is drawn from a population and asked how much...

5. A random sample of 120 people is drawn from a population and asked how much time each week they spend watching television. The population has a mean of 187 minutes with a standard deviation of 32 minutes.

(a) Find the mean and standard error of the sampling distribution of ¯x.

(b) What is the probability that this sample will have a mean that is at least 192 minutes?

(c) What proportion of all samples of size 120 will have a mean that is at least 192 minutes? (d) What is the 90’th percentile

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

a) Since the sample size is large, by Central Limit Theorem the sampling distribution of mean approaches normal distribution (as n increases)

so mean= 187 and

SD=32/10.95445

{square root of 120 is 10.95445}

b) The probability that the sample mean is at least 192 minutes is given by P[X>=192]

=0.04348216

c) Proportion of samples of size 120 that will have a mean that is at least 192 minutes is 120*0.04348216 = 5.217859

ie, 5 percent

d) 90 th percentile is 201.0387

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
a) Consider random samples of size 56 drawn from population A with proportion 0.77 and random...
a) Consider random samples of size 56 drawn from population A with proportion 0.77 and random samples of size 78 drawn from population B with proportion 0.67 . Find the standard error of the distribution of differences in sample proportions, p^A-p^B. Round your answer for the standard error to three decimal places. standard error = ___________________ b) Consider random samples of size 470 drawn from population A with proportion 0.55 and random samples of size 210 drawn from population B...
Consider random samples of size 86 drawn from population A with proportion 0.47 and random samples...
Consider random samples of size 86 drawn from population A with proportion 0.47 and random samples of size 64 drawn from population B with proportion 0.19 . Find the standard error of the distribution of differences in sample proportions, p^A-p^B. Round your answer for the standard error to three decimal places.
A survey was taken of 383 students that asked the question how much time they spent...
A survey was taken of 383 students that asked the question how much time they spent watching television in a day (in minutes). Suppose this sample study follows a Normal distribution with a sample mean x-bar = 118 minutes. Also suppose the population has a standard deviation σ = 53 minutes. Determine a 96% confidence interval for the mean television watching time. A. 112.67 to 123.31 B. 117.86 to 118.14 C. 112.44 to 123.56 D. 111.70 to 124.30
A random sample of 58 randomly selected people were asked how much they spend on their...
A random sample of 58 randomly selected people were asked how much they spend on their grocery bill each week. The mean was $115.36 with a standard deviation of $16.6. Find a 95% confidence interval for the true population mean amount spent on groceries each week. Report the answer accurate to four decimal places.
Consider random samples of size 82 drawn from population A with proportion 0.45 and random samples...
Consider random samples of size 82 drawn from population A with proportion 0.45 and random samples of size 64 drawn from population B with proportion 0.11 . (a) Find the standard error of the distribution of differences in sample proportions, p^A-p^B. Round your answer for the standard error to three decimal places. standard error = Enter your answer in accordance to the question statement       (b) Are the sample sizes large enough for the Central Limit Theorem to apply?...
Consider random samples of size 58 drawn from population A with proportion 0.78 and random samples...
Consider random samples of size 58 drawn from population A with proportion 0.78 and random samples of size 76 drawn from population B with proportion 0.68 . (a) Find the standard error of the distribution of differences in sample proportions, p^A-p^B. Round your answer for the standard error to three decimal places. standard error = Enter your answer in accordance to the question statement (b) Are the sample sizes large enough for the Central Limit Theorem to apply? Yes No
A sample of 120 is drawn from a population with a proportion equal to 0.50. Determine...
A sample of 120 is drawn from a population with a proportion equal to 0.50. Determine the probability of observing between 54 and 72 successes.
A random sample is drawn from a population with mean μ = 52 and standard deviation...
A random sample is drawn from a population with mean μ = 52 and standard deviation σ = 4.3. a. Is the sampling distribution of the sample mean with n = 13 and n = 39 normally distributed? Yes, both the sample means will have a normal distribution. No, both the sample means will not have a normal distribution. No, only the sample mean with n = 13 will have a normal distribution. No, only the sample mean with n...
Q.6. (a) A random sample is drawn from a population with a known standard deviation of...
Q.6. (a) A random sample is drawn from a population with a known standard deviation of 2.0. Find the standard error (SE) of the sample mean if the sample size is (i) 16, (ii) 36, (iii) 81. (b) If the size of sample is 36 and the standard error of the mean is 2, what should be the size of the sample if the standard error is reduced to 1.2? solve the above problem step by step in proper format
A random sample is drawn from a population with mean μ = 53 and standard deviation...
A random sample is drawn from a population with mean μ = 53 and standard deviation σ = 4.4. [You may find it useful to reference the z table.] a. Is the sampling distribution of the sample mean with n = 13 and n = 38 normally distributed? Yes, both the sample means will have a normal distribution. No, both the sample means will not have a normal distribution. No, only the sample mean with n = 13 will have...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT