Question 13 pts

The American Bankers Association Community Bank Insurance Survey for 20xx had responses from 151 banks. A Community Bank is defined as a bank with assets of $1 billion or less. One question on the survey was, "Is your financial institution a Community Bank (yes or no)." Of the respondents, 80 replied "yes." Let p equal the true proportion of all banks in the U.S. that are Community Banks. What is the count X of "successes"?

0 151

0 80

Question 24 pts

The American Bankers Association Community Bank Insurance Survey for 20xx had responses from 174 banks. A Community Bank is defined as a bank with assets of $1 billion or less. One question on the survey was, "Is your financial institution a Community Bank (yes or no)." Of the respondents, 52 replied "yes." Let p equal the true proportion of all banks in the U.S. that are Community Banks.

What was the sample proportion?

Round your answer to 2 decimal places of accuracy.

Question 35 pts

You are conducting a quality control test for bolts delivered by your supplier. The diameter of the bolt must be within 0.01 mm. of the size of pre-drilled holes in shaped metal parts for the machine that your company manufactures. Suppose that the true proportion of bolts that meet your specs is p 0.73. What is the minimum sample size required for the sample proportion to have approximately a Normal distribution?

Round your answer to the nearest integer. (Note: in practice, you should round up. However, except for small minimum sample sizes, the two methods of rounding have about the same effect on the results.)

Question 47 pts

A sample of 140 potential customers was asked to use your new product and the product of the leading competitor. After one week, they were asked to indicate which product they preferred. Let X the number of customers who said that they preferred your product. In the sample, X 34.

Calculate the lower end of a 95% confidence interval for p, the proportion of potential customers who prefer your product to that of your competitor. Apply the largesample confidence interval procedure. Calculate z* in Excel, and do not round in your intermediate calculations.

Express your answer in decimal form to two decimal places of accuracy.

Question 57 pts

As part of a quality improvement program, your mail-order company is evaluating the process of filling customer orders. According to company standards, an order is shipped on time if it is sent within two working days of the time it is received. You select an SRS of 254 of the 6,000 orders received in the past month for an audit. The audit reveals that 173 of these orders were shipped on time.

Calculate the upper end of a 99% confidence interval for p, the population proportion of orders in the last month that were shipped on time. Apply the large-sample confidence interval procedure. Calculate z* in Excel, and do not round in your intermediate calculations.

Express your answer in decimal form to two decimal places of accuracy.

question 67 pts

Your company manufacturers electronic thermostats. Each thermostat uses a temperature sensitive switch to turn the heating/cooling system that it controls on or off. Periodically, you inspect a batch of switches from a large shipment of switches to verify quality of the work of your supplier. Let X - number of failures in the sample. Let p the true proportion of failing switches in the shipment.

Suppose that in an SRS of 124 switches, you find 3 failures.

Calculate the upper end of a 99% confidence interval for p, the population proportion of failing switches. Calculate z* in Excel, and do not round in your intermediate calculations. Use the Wilson Estimate to calculate the interval.

Express your answer in decimal form to two decimal places of accuracy.

Question 76 pts

You plan to survey an SRS of potential customers who have been asked to use your new product and the product of a leading competitor for one week. After one week, you will ask each subject in your sample which product they preferred. Let n be the sample size, and X count of number of subjects who state that they prefer your product.

Assume that you plan to construct a large-sample confidence interval for p, the true proportion of all potential customers who would prefer your product to that of your competitor. The level of confidence will be 99%; for this pro blem, use z* 2.576 as your critical value. For planning purposes, you are willing to use a guess of po 0.5 to find the sample size necessary to achieve a margin of error of 0.052 or less.

Round your answer to the nearest integer. (Note: in practice, you should round up. However, except for small minimum sample sizes, the two methods of rounding have about the same effect on the results.)

Question 87 pts

Consider an SRS of a batch of switches from a large shipment of switches. The sample size is n 252. Let p the true proportion of switches in the shipment that are defective. The null hypothesis is that only 5% of switches are bad. Because we are only concerned with evidence that switches are more defective than usual, the following one-sided test is appropriate: Ho: p 0.05 versus the alternative HA: p > 0.05.

Suppose that X 30 switches are bad. Calculate the large-sample z-statistic.

Round your answer to 3 decimal places of accuracy. If z is negative, then include the minus sign.

Your company sells a tap water filter. The filter sits on a one-gallon carafe. The customer runs tap water (or water from any source) into the top of the filter mechanism. Filtered water then drains into the carafe. You hire an independent testing company to compare the efficiency of your filter versus the EPA standards. One key Tieasurement is percent of heavy metals that remain after filtering.

The testing company draws an SRS of size n 200 of your filters out of a large batch recently manufactured and runs highly contaminated water through each filter. The level and mix of contaminants is the same for each filter that is tested. Let X be the number of filters that meet the EPA standards (i.e., that have lower heavy metal contamination than the EPA standard).

Let p proportion of all of your company's filters in the current batch that fail to meet the standard. The null hypothesis is that Ho: p 0.05 versus HA: p 0.05. This value for po was the percent of your filters that failed the test the last time that the filters were tested (i.e., 5% failed to meet the standard). X number of filters in the sample that failed to meet the standard. Suppose that X 15. What is the P-value for this hypothesis test?

0 0.975

0 0.150

0 0.052

0 0.948

0 0.105

Question 97 pts

Your company sells a tap water filter. The filter sits on a one-gallon carafe. The customer runs tap water (or water from any source) into the top of the filter mechanism. Filtered water then drains into the carafe. You hire an independent testing company to compare the efficiency of your filter versus the EPA standards. One key measurement is percent of heavy' metals that remain after filtering.

The testing company draws an SRS of size n 200 of your filters out of a large batch recently manufactured and runs highly contaminated water through each filter. The level and mix of contaminants is the same for each filter that is tested. Let X be the number of filters that meet the EPA standards (i.e., that have lower heavy metal contamination than the EPA standard).

Let p proportion of all of your company's filters in the current batch that fail to meet the standard. The null hypothesis is that Ho: p 0.05 versus HA: p 0.05. This value for po was the percent of your filters that failed the test the last time that the filters were tested (i.e., 5% failed to meet the standard).

X number of filters in the sample that failed to meet the standard. Suppose that X 15. What is the P-value for this hypothesis test?

0 0.975

0 0.150

0 0.052

0 0.948

0 0.105

Question 105 pts

Consider a two-sided hypothesis test, Ho: p po versus HA: p PO, where p is the true population proportion of "successes." Let po 0.45. Let X 70, number of

"successes" in an SRS of size n 200. Suppose that you perform a large sample z-significance test for p. The P-value is 0.004. Interpret this result; select the best choice from the list. (Note: no calculations are required.)

O We cannot draw any conclusions about the population proportion when the sample proportion is this close to the value in the null hypothesis.

O The probability is less than 1% that we would observe a sample proportion 0.35 that is this far from 0.45 just by random chance, assuming that the true proportion is 0.45. Thus, we have strong evidence that the true population proportion is not 0.45.

C) The probability is about 1% that we would observe a P-value that is as small as 0.35 just by random chance. Thus, the evidence is strong that the true population proportion is 0.35.

O The probability is about 1% that we would observe a sample proportion 0.35 that is this far from 0.45 just by random chance, assuming that the true proportion is 0.45. Thus, we have insufficient evidence that the true population proportion is not 0.45.

C) The probability is about 1% that we would observe a P-value that is as small as 0.35 just by random chance. Thus, we have evidence that the true population proportion is 0.45.

Question 116 pts

Consider a survey of customers who bought a Christmas tree during the holiday season. Respondents were classified as either living in a rural area (population #1) or living in an urban area (population #2). Each respondent was asked whether they purchased a natural tree or an artificial tree. The population proportions in this study are the proportion of persons who bought a natural tree ("success"). (Assume, for this analysis, that the survey was conducted by drawing an SRS from rural dwellers who bought a Christmas tree and an independent SRS from urban dwellers who bought a tree.)

The sample from rural dwellers who bought a tree had a sample size ni 172 and count of "successes" (i.e., number who bought a natural tree) of Xl 63.

The sample from urban dwellers who bought a tree had a sample size n2 237 and count of "successes" (i.e., number who bought a natural tree) of 125.

What is the difference of sample proportions, D PI pp.

Round your answer to 3 decimal places of accuracy. If the difference is negative, include a minus sign as part of your answer.

Question 126 pts

Consider a survey of customers who bought a Christmas tree during the holiday season. Respondents were classified as either living in a rural area (population #1) or living in an urban area (population #2). Each respondent was asked whether they purchased a natural tree or an artificial tree. The population proportions in this study are the proportion of persons who bought a natural tree ("success"). (Assume, for this analysis, that the survey was conducted by drawing an SRS from rural dwellers who bought a Christmas tree and an independent SRS from urban dwellers who bought a tree.)

The sample from rural dwellers who bought a tree had a sample size ni 159 and count of "successes" (i.e., number who bought a natural tree) of Xl 70.

The sample from urban dwellers who bought a tree had a sample size n2 214 and count of "successes" (i.e., number who bought a natural tree) of 108.

What is the standard error of the difference D p2?

Round your answer to 3 decimal places of accuracy.

Question 137 pts

Consider a survey of customers who bought a Christmas tree during the holiday season. Respondents were classified as either living in a rural area (population #1) or living in an urban area (population #2). Each respondent was asked whether they purchased a natural tree or an artificial tree. The population proportions in this study are the proportion of persons who bought a natural tree ("success"). (Assume, for this analysis, that the survey was conducted by drawing an SRS from rural dwellers who bought a Christmas tree and an independent SRS from urban dwellers who bought a tree.)

The sample from rural dwellers who bought a tree had a sample size ni 175 and count of "successes" (i.e., number who bought a natural tree) of Xl 90.

The sample from urban dwellers who bought a tree had a sample size n2 250 and count of "successes" (i.e., number who bought a natural tree) of 80.

Construct the level C 99% confidence interval for the difference in population means, pi - p2. Also, state the inference about the difference.

0 (0.07, 0.32) With 99% confidence, the difference in population proportions is greater than zero.

O (0.00, 0.19) With 99% confidence, the difference in population proportions is not greater than zero.

O (0.12, 0.27) With 99% confidence, the difference in population proportions is greater than zero.

0 (0.10, 0.29) With 99% confidence, the difference in population proportions is greater than zero.