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# Statistics - Questions for a brainbox! watch

1. Hello,

I have 10 questions which I'm stuck on, can anyone help me out?

1) In an effort to estimate the mean amount spent per customer for dinner at a major Atlanta restaurant, data were collected for a sample of n customers over a three-week period, where

n = 55.

The sample mean of the collected data is

xbar = 26.91 dollars.

Assume that the population standard deviation is

sigma = 3.16.

Then the 95% confidence interval for the population mean is

2) In an effort to estimate the mean amount spent per customer for dinner at a major Atlanta restaurant, data were collected for a sample of n customers over a three-week period, where

n = 25.

The sample mean of the collected data is

xbar = 29.76 dollars,

and the sample standard deviation is

s = 4.44.

Then the 95% confidence interval for the population mean is

3) A random sample of 10 items from a Normally distributed population is given below:

3.35, 2.44, 1.61, 4.42, 1.75, .16, 4.75, 4.2, 2.55, 3.25.

A 90% confidence interval for the population mean is

4) Assuming that the following sample of 12 numbers arise from a Normal distribution with mean u and standard deviation sigma, where

sigma = 5.62, and the 12 samples are:

103.6, 101.92, 101.62, 98.19, 108.4, 108.01, 98.38, 98.25, 95.2, 100.72, 99.89, 97.71.

It was believed that the population mean u is 100. You tested the null hypothesis H0 : u = 100 against the two-sided alternative hypothesis H1 : u not equal to 100. What is the p-value of the test statistic?

The p-value is

5) Young Adult magazine states the following hypotheses about the mean age of its subscribers: H0: u = u0 and H1: u not equal to u0. If the manager conducting the test will permit a probability beta of making a Type II error when the true mean age is u1, what sample size should be selected? Assume population standard deviation is sigma and an alpha level of significance is chosen, where

u0 = 30, u1 = 31, sigma = 6, alpha = .05, beta = .11.

Then the sample size should be..

6) An automobile mileage study tested the following hypotheses:
H0: u = u0 mpg, i.e. Manufacturer's claim supported.
H1: u < u0 mpg, i.e. Manufacturer's claim rejected and the average mileage per gallon is less than stated, where u0 = 27.
Suppose the population standard deviation is sigma = 4.53,
and at a 0.02 significance level, what sample size would be recommended if the researcher wants an 80% chance of detecting that u < u0 miles per gallon when it is actually u1, where
u1 = 26 ?

The sample size would be:

7) A bath soap manufacturing process is designed to produce a mean of 120 bars of soap per batch. Quantities over or under the standard are undesirable. A sample of ten batches shows the following numbers of bars of soap.

122, 125, 109, 127, 124, 121, 113, 116, 118, 114.

Using a 0.01 level of significance, test to see whether the sample results indicate that the manufacturing process is functioning properly.

Then the p-value of the test statistic is:

8) The monthly rent for a two-bedroom apartment in a particular city is reported to average \$550. Suppose we want to test H0: u = 550 versus H1: u not equal to 550 at a 5% significant level. A sample of 26 two-bedroom apartments is selected with the sample mean xbar and sample standard deviation s, where

xbar = 574, s = 42.

Then the p-value of the test statistic is:

9) In making bids on building projects, Sonneborn Builders Inc. assumes construction workers are idle no more than 15% of the time. Hence, for a normal eight-hour shift, the mean idle time per worker should be 72 minutes or less per day. A sample of 25 construction workers had a mean idle time of xbar minutes per day and the sample standard deviation was s minutes, where

xbar = 86, s = 23.

Using a 0.05 level of significance test H0: u = 72 against u > 72.

The p-value of the test statistic is

10) The manager of the Keeton Department Store has assumed that the mean annual income of the store's credit-card customers is H0: u = \$28000 per year. A sample of 28 credit-card customers shows a sample mean of xbar and a sample standard deviation of s, where

xbar = 27201, s = 2908.

At the 0.05 level of significance, should we conclude that u < \$28000?

The p-value of the test statistic is:

Any help would be appreciated!!
2. (Original post by tubsey123)
hello,

i have 10 questions which i'm stuck on, can anyone help me out?

1) in an effort to estimate the mean amount spent per customer for dinner at a major atlanta restaurant, data were collected for a sample of n customers over a three-week period, where

n = 55.

The sample mean of the collected data is

xbar = 26.91 dollars.

Assume that the population standard deviation is

sigma = 3.16.

Then the 95% confidence interval for the population mean is

2) in an effort to estimate the mean amount spent per customer for dinner at a major atlanta restaurant, data were collected for a sample of n customers over a three-week period, where

n = 25.

The sample mean of the collected data is

xbar = 29.76 dollars,

and the sample standard deviation is

s = 4.44.

Then the 95% confidence interval for the population mean is

3) a random sample of 10 items from a normally distributed population is given below:

3.35, 2.44, 1.61, 4.42, 1.75, .16, 4.75, 4.2, 2.55, 3.25.

A 90% confidence interval for the population mean is

4) assuming that the following sample of 12 numbers arise from a normal distribution with mean u and standard deviation sigma, where

sigma = 5.62, and the 12 samples are:

103.6, 101.92, 101.62, 98.19, 108.4, 108.01, 98.38, 98.25, 95.2, 100.72, 99.89, 97.71.

It was believed that the population mean u is 100. You tested the null hypothesis h0 : U = 100 against the two-sided alternative hypothesis h1 : U not equal to 100. What is the p-value of the test statistic?

The p-value is

5) young adult magazine states the following hypotheses about the mean age of its subscribers: H0: U = u0 and h1: U not equal to u0. If the manager conducting the test will permit a probability beta of making a type ii error when the true mean age is u1, what sample size should be selected? Assume population standard deviation is sigma and an alpha level of significance is chosen, where

u0 = 30, u1 = 31, sigma = 6, alpha = .05, beta = .11.

Then the sample size should be..

6) an automobile mileage study tested the following hypotheses:
H0: U = u0 mpg, i.e. Manufacturer's claim supported.
H1: U < u0 mpg, i.e. Manufacturer's claim rejected and the average mileage per gallon is less than stated, where u0 = 27.
Suppose the population standard deviation is sigma = 4.53,
and at a 0.02 significance level, what sample size would be recommended if the researcher wants an 80% chance of detecting that u < u0 miles per gallon when it is actually u1, where
u1 = 26 ?

The sample size would be:

7) a bath soap manufacturing process is designed to produce a mean of 120 bars of soap per batch. Quantities over or under the standard are undesirable. A sample of ten batches shows the following numbers of bars of soap.

122, 125, 109, 127, 124, 121, 113, 116, 118, 114.

Using a 0.01 level of significance, test to see whether the sample results indicate that the manufacturing process is functioning properly.

Then the p-value of the test statistic is:

8) the monthly rent for a two-bedroom apartment in a particular city is reported to average \$550. Suppose we want to test h0: U = 550 versus h1: U not equal to 550 at a 5% significant level. A sample of 26 two-bedroom apartments is selected with the sample mean xbar and sample standard deviation s, where

xbar = 574, s = 42.

Then the p-value of the test statistic is:

9) in making bids on building projects, sonneborn builders inc. Assumes construction workers are idle no more than 15% of the time. Hence, for a normal eight-hour shift, the mean idle time per worker should be 72 minutes or less per day. A sample of 25 construction workers had a mean idle time of xbar minutes per day and the sample standard deviation was s minutes, where

xbar = 86, s = 23.

Using a 0.05 level of significance test h0: U = 72 against u > 72.

The p-value of the test statistic is

10) the manager of the keeton department store has assumed that the mean annual income of the store's credit-card customers is h0: U = \$28000 per year. A sample of 28 credit-card customers shows a sample mean of xbar and a sample standard deviation of s, where

xbar = 27201, s = 2908.

At the 0.05 level of significance, should we conclude that u < \$28000?

The p-value of the test statistic is:

Any help would be appreciated!!
lol swansea
3. Definitely statistics work tomorrow at 3:00pm! I'm in the same boat - this is hard!! Thank god I only need a mark to pass module. Good luck!

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