Statistics Exam 2

A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressing is working properly when 8 ounces are dispensed. The standard deviation of the process is known to be 0.15 ounces. A sample of 48 bottles is selected periodically, and the filling line is stopped if there is evidence that the mean amount dispensed is different from 8 ounces. Suppose that the mean amount dispensed in a particular sample of 48 bottles is 7.983 ounces. Calculate the test statistic.

-0.785

A fish hatchery spawns and raises fish to stock natural lakes. The hatchery has a target fish length of 8 inches or more. A recently completed production batch that was sampled revealed the following: 40 fish sampled resulted in a sample mean length of 7.95 inches and a standard deviation of 0.3 inches. Test, at a 5% level of significance, whether this batch has met the hatchery's production goal. Enter your answer as the "data" value computed in step 5. Round answer to two decimals, and include a negative sign if the answer is negative.

-1.05

Spaulding is the leading maker for basketballs in the US. Spaulding prides itself on the quality that its basketballs have the right amount of bounce when it is taken out of the packaging. They want their product to be ready for use upon opening. The air pressure of a particular ball has a target value of 7.8 PSI. Suppose the basketballs have a normal distribution with a standard deviation of 0.25 PSI. When a shipment of basketballs arrive, a retailer takes a sample of 9 balls from the shipment and measures their PSI to see if it meets the target value, and finds the mean to be 7.7 PSI. Determine, through hypothesis testing at a 5% significance level using the critical value approach, whether or not the shipment meets the pressure requirement. For your answer in this problem - give the calculated test statistic (the "data" value) you would come up with in step 5 of the hypothesis testing process

-1.20

A random sample of size 1,000 is taken from a population where p = .20. Find the probability that the sample proportion will be < .18.

.0571

If we select two balls, with replacement, from a box containing two balls, numbered 1 and 0, and then average the values that appear on the selected balls, the possible means are ________________.

0, 0.5 & 1

Last year, a comprehensive report stated that 33% of businesses in northeast of Ohio were considered highly profitable. This year, based on a sample of 48 business owners, a survey your team conducted indicated that 25 businesses were highly profitable. Based on this sample, would you conclude that the proportion of businesses that are highly profitable increased from last year with a statistical significance? Use a statistical hypothesis test to determine this, using a 1% significance level. (Note from the Instructor - Think about this concept for your studying purposes) For you answer in this problem - give the calculated p-value you would come up with in step 5 of the hypothesis testing process. Give answer to 4 decimal places.

0.0026

Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.2 ounces. The weights of the sugar bags are normally distributed. What is the probability that 16 randomly selected packages will have a weight in excess of 16.075 ounces?

0.0668

According to Smith Travel Research, the average hotel price in the United States in 2009 was $97.68. Assume the population standard deviation is $18.00 and that a random sample of 35 hotels was selected. What is the probability that a randomly selected sample mean will be more than $102?

0.0778

It is commonly known that approximately 10% of the population is left-handed. A large golf club manufacturing firm would like to estimate the proportion of left-handed golfers in order to plan their schedule of golf club production. Assume that the manufacturer collected a sample of 200 golfers. What is the probability that more than 12% of the golfers in the sample are left-handed?

0.1736

A Midwestern community college has 240 full-time employees that are currently covered under the school's health care plan. The average out-of-pocket cost for the employees on the plan is $1,880 with a standard deviation of $515. The college is performing an audit of its health care plan and has randomly selected 30 employees to analyze their out-of-pocket costs. What is the probability that the sample mean will be between $1,900 and $1,950?

0.1872

If you live in California, the decision to buy earthquake insurance is an important one. A survey revealed that only 133 of 337 randomly selected residences in one California county were protected by earthquake insurance. What is the p-value associated with the test statistic calculated to test the claim that less than 40% of the county residents are protected by earthquake insurance.

0.4207

The Social Media and Personal Responsibility Survey in 2010 found that 69% of parents are "friends" with their children on Facebook. A random sample of 140 parents was selected. What is the probability that between 96 and 105 parents from this sample are "friends" with their children on Facebook?

0.4780

A national survey of 250 adults was conducted and it concluded that 55% of that sample believe that big-time college sports programs corrupt the process of higher education. What is the upper boundary value of the 99% confidence interval for the population proportion?

0.631

According to the National Association of Realtors, 44% of U.S. homes sold in March 2010 were purchased by first-time buyers. A random sample of 175 people who just purchased homes is selected. What is the probability that less than 80 of them are first-time buyers?

0.6736

In publishing the results of some research work, the following values of the coefficient of correlation were listed. Which one would appear to be incorrect?

1.25

Given the following information about a hypothesis test of the difference between two means based on independent random samples, what is the calculated value of the test statistic? Assume that the samples are obtained from normally distributed populations having equal variances.HA: µA> µB, Sample Mean 1 = 12, Sample Mean 2 = 9, s1 = 5, s2 = 3, n1 = 13, n2 = 10.

1.674

A fish hatchery spawns and raises fish to stock natural lakes. The hatchery has a target fish length of 8 inches or more. A recently completed production batch that was sampled revealed the following: 40 fish sampled resulted in a sample mean length of 7.95 inches and a standard deviation of 0.3 inches. Test, at a 5% level of significance, whether this batch has met the hatchery's production goal. Enter your answer as the critical ("crit") value computed in step 4. Round answer to three decimals, and include a negative sign if the answer is negative.

1.685

Calculate the upper bound for a 90% confidence interval forμ where σ is unknown and s is calculated to be 3 and x⎯⎯ = 12 and sample size is n = 80.

12.553

Calculate the upper bound for a 95% confidence interval forμ where σ is known to be 2 and x⎯⎯ (x bar) = 13 and sample size is n = 85. (Answer to 3 decimal places)

13.425

According to the Beverage Marketing Corporation, the per capita consumption of bottled water in 2009 was 2.3 gallons per month. Assume the standard deviation for this population is 0.75 gallons per month. Consider a random sample of 36 people. What specific amount represents the number of gallons of water that 37% of all samples from this distribution have a value less than?

2.259

Last year, a comprehensive report stated that 33% of businesses in northeast of Ohio were considered highly profitable. This year, based on a sample of 48 business owners, a survey your team conducted indicated that 25 businesses were highly profitable. Based on this sample, would you conclude that the proportion of businesses that are highly profitable increased from last year with a statistical significance? Use a statistical hypothesis test to determine this, using a 1% significance level. (Note from the Instructor - Think about this concept for your studying purposes) For you answer in this problem - give the calculated test statistic you would come up with in step 5 of the hypothesis testing process.

2.79

A regression between foot length (response variable in cm) and height (predictor variable in inches) for 33 students resulted in the regression equation "FootLength = 10.9 + 0.23(Height)". One student in the sample was 73 inches tall. What is the predicted foot length for this student?

27.69 cm

A random sample of 80 companies who announced corrections to their balance sheets took a mean time of 8.1 days for the time between balance sheet construction and the complete audit. The standard deviation for times was known to be 1.3 days. What is the critical (table) value for α = .001 to test the claim that μ is greater than 7.5 days.

3.09

Which of the following is/are (an) example(s) of a hypothesis in the context of statistics? 1. The unemployment rate is greater than SP. 2. An airline claims that its "on-time" arrival rate is greater than 95%. 3. A mayor touts the fact that wind turbines provide greater than 20g of the power local community. 4. A manager of a popular restaurant claims that her restaurant's table turnaround time has decreased within the last quarter by at least 10 minutes.

All Four

A confidence interval increases in width as... a. the level of confidence increases b. n decreases c. s increases all of these d. all of these

All of these

As the margin of error decreases, the width of the confidence interval ______________.

Decreases

Testing the equality of means at alpha = .05, where sample 1 has data: 16, 14, 19, 18, 19, 20, 15, 18, 17, 18, and sample 2 has data: 13, 19, 14, 17, 21, 14, 15, 10, 13, 15 (Assume equal population variances), we determine that we can reject the null hypothesis.

False

When the population is normally distributed and the population standard deviation σ is unknown, then for any sample size n, the sampling distribution of x-bar is based on the z distribution.

False

Spaulding is the leading maker for basketballs in the US. Spaulding prides itself on the quality that its basketballs have the right amount of bounce when it is taken out of the packaging. They want their product to be ready for use upon opening. The air pressure of a particular ball has a target value of 7.8 PSI. Suppose the basketballs have a normal distribution with a standard deviation of 0.25 PSI. When a shipment of basketballs arrive, a retailer takes a sample of 9 balls from the shipment and measures their PSI to see if it meets the target value, and finds the mean to be 7.7 PSI. Determine, through hypothesis testing at a 5% significance level using the critical value approach, whether or not the shipment meets the pressure requirement.

Ha: mu /= (not-equal-to) 7.8

As the standard deviation increases, the sample size _____________ to achieve a specified level of confidence.

Increases

Assuming a fixed sample size, as α (Type I error) decreases, β (Type II error) ___________.

Increases

For non-normal populations, as the sample size (n) ___________________, the distribution of sample means approaches a(n) ________________ distribution.

Increases, Normal

If the sample sizes are different in a two-samp1e hypothesis test, then the samples must be _____

Independent

For the following hypothesis test where H0: µ ≤ 10 vs. Ha: µ > 10, we reject H0 at level of significance α and conclude that the true mean is greater than 10 when the true mean is really 14. Based on this information we can state that we have:

Made a correct decision

The width of a confidence interval will be:

Narrower for 90% confidence than 95% confidence.

A(n) _________ hypothesis is the statement that is being tested. It usually represents the status quo and it is not rejected unless if there is convincing sample evidence that it is false.

Null

Unlike the _____ hypothesis, the _____ hypothesis is not assumed to be true at the outset of the hypothesis test. It is only supported if the sample evidence is significant.

Null, Alternative

If a one-sided null hypothesis is rejected at a given significance level, then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will _________ be rejected at the same significance level.

Sometimes

If a one-sided null hypothesis is rejected for a single mean at a given significance level, the corresponding two-sided null hypothesis will ________ be rejected at the same significance level

Sometimes

There is little difference between the values of tα/2 and zα/2 when:

The sample size is large

In a past General Social Survey, a random sample of men and women answered the question "Are you a member of any sports clubs?" Based on the sample data, 95% confidence intervals for the population proportion who would answer "yes" are .13 to .19 for women and .247 to .33 for men. Based on these results, you can reasonably conclude that ...

There is a difference between the proportions of American men and American women who belong to sports clubs.

If we have a sample size of 100 and the estimate of the population proportion is .10, we can estimate the sampling distribution of p-hat with a normal distribution.

True

It can be established at alpha = .05 that a majority (more than 50%) of students favor the plus/minus grading system at a university if in a random sample of 500 students, 270 favor the system.

True

The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a Z test to test the null hypothesis that the mean tensile strength is 800 pounds per square inch. The calculated Z test statistic is a positive value that leads to a p-value of .045 for the test. If the significance level (α) is .05, the null hypothesis would be rejected.

True

The sampling distribution of a sample statistic is the probability distribution of the population of all possible values of the sample statistic.

True

The sampling distribution of a statistic is a probability distribution for all of the possible values of a sample statistic that can be derived from samples of a given size.

True

When the margin of error is added to and subtracted from the sample mean an interval is formed that will contain μ with probability of (1 - α).

True

The production manager for the XYZ manufacturing company is concerned that the customer orders are being shipped late. He asked one of his planners to check the timeliness of shipments. The planner randomly selected 1000 orders and found that 120 orders were shipped late. Construct the 95% confidence interval for the proportion of orders shipped late.

[.0999 .1401]

An insurance analyst working for a car insurance company would like to determine the proportion of accident claims covered by the company. A random sample of 200 claims shows that the insurance company covered 80 accident claims while 120 claims were not covered. Construct a 90% confidence interval estimate of the true proportion of claims covered by the insurance company.

[.343 .457]

A random sample of size 30 from a normal population yields a sample mean of 32.8. The population standard deviation is known to be 4.51. Construct a 95 percent confidence interval for the mean.

[31.19 34.41]

A sample of 12 items yields a mean of 48.5 grams and s = 1.5 grams. Assuming a normal distribution for the population, construct a 90 percent confidence interval for the mean weight.

[47.722 49.278]

The diameter of small Nerf balls manufactured at a factory in China is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls is selected. Find the interval that contains the middle 95.44% of the sample means.

[5.16 5.24]

An indication of no linear relationship between two variables would be...

a correlation coefficient equal to 0

Consider a sampling distribution formed based on n=3. The standard deviation of the population of all sample means std. deviation is _________ less than the standard deviation of the population of individual measurements std. deviation

always

Correlation does not imply __________.

causation

The ___________ method can be used to decide whether or not to reject the null hypothesis by looking up a value on the table for each distribution (t, z, F, etc.) and comparing it to the test statistic.

critical value

According the Central Limit Theorem, a sample size ______________ is large enough to assume that the sample mean is approximately normal.

greater than 30

A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: y = 120 + 5x . This implies that if the height is increased by 1 inch, the weight is expected to...

increase by 5 pounds

Consider the following null and alternative hypotheses. Ho: μ ≤ 101 Ha: μ > 101 These hypotheses _______________.

indicate a one-tailed test with a rejection area in the right tail

Which of the following is an advantage of a confidence interval estimate over a point estimate for a population parameter?

interval estimates taken into account the fact that the statistic being used to estimate the population parameter is a random variable

If all the points in a scatterplot lie on the least squares regression line, then the coefficient of correlation...

must be either -1.0 or 1.0

If the coefficient of correlation is a positive value, then the corresponding regression equation...

must have a positive slope

The t-distribution has __________ degrees of freedom.

n - 1

Assuming that the null hypothesis is true, the ______________ is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data.

p-value

The standard error of the mean is equal to the standard deviation of the population divided by the _______________________.

square root of the sample size

A correlation coefficient describes the of dependency between two quantitative variables.

strength and direction

When we replace σ with the sample standard deviation (s), we introduce a new source of variability and the sampling distribution becomes the __________

t distribution

Confidence intervals are a function of which of the following three things:

the data in the sample; the confidence level; the sample size

Which of the following statements is NOT true about the standard error of a statistic?

the standard error increases as the sample size increases

1. For a left-tailed hypothesis test, the p-value is the area under the normal curve _____

to the left of the test statistic (the test's "data" value)

Which of the following represents a significance level?

α (alpha)

A financial analyst working for a financial consulting company wishes to find evidence that the average price-to-earnings ratio in the consumer industry is higher than average price-to-earnings ratio in banking industry. The alternative hypothesis is:

μconsumer> μbanking