Stats test 2

.Assuming a fixed sample size, as α (Type I error) decreases, β (Type II error) ___________. A Increases B Decreases C Stays the same D Randomly fluctuates

A

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. A 0.785 B-1.57 C -3.04 D 1.57 E 0.785

A

As the standard deviation increases, the sample size _____________ to achieve a specified level of confidence. A Increases B Devreases C Remains the same

A

Consider a sampling distribution formed based on n=3. The standard deviation of the population of all sample means "sample deviation x-bar" is ——- less than the standard deviation of the population of individual measurements standard deviation A. Always B. Sometimes C. Never D. Can't determine with provided

A. Always

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 A 2.575 B 3.09 C -1.96 D -2.575 D -3.09

B

For non-normal populations, as the sample size (n) ___________________, the distribution of sample means approaches a(n) ________________ distribution. A Decreases, Uniform B Increases, Normal C Decreases, Normal D Increases, Uniform E Increases, Exponential

B

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. A 1.96 B 1.674 C 1.5 D 1.063 E 2.823

B

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 A. Always B. Sometimes C. Never

B

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. A(.1135 - .1265) B(0.999 - .1401) C(.0619 - .1781) D(.1011 - .1389)

B

There is little difference between the values of tα/2 and zα/2 when: A The sample size is small B The sample size is large C The sample mean is small D The sample mean is large E The sample standard deviation is small

B

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. A. Alternative, null B. Null, alternative C. Alternate, zero D. Alternative, alternative

B.

A correlation coefficient describes the —- of the dependency between two quantitative variables A. Strength B. Direction C. Strength and direction D. Causation

C

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: A μconsumer< μbanking B μconsumer≠ μbanking C μconsumer> μbanking Dμconsumer= μbanking Eμconsumer≤ μbanking

C

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. A .9429 B .0793 C .0571 D .2643

C

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. A Research B Alternative C Null D Chi-square

C

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. A α B β C p-value D Type 1 error

C

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: A Made a Type I error B Made a Type II error C Made a correct decision D Increased the power of the test

C

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. A(5.04 - 5.36) B(5.18 - 5.22) C(5.16 - 5.24) D(5.07 - 5.33)

C

The width of a confidence interval will be: A Narrower for 99% confidence than 95% confidence. B Wider for a sample size of 100 than for a sample size of 50 C Narrower for 90% confidence than 95% confidence. D Wider when the sample standard deviation (s) is small than when s is large.

C

If the sample sizes are different in a two-sample hypothesis test, then the samples must be ? A. Dependent B. Normally distributed C. Independent D. Unreliable

C.

A confidence interval increases in width as A. The level of confidence increases B. N decreases C. S increases D. All of these

D

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. A 23.96 - 41.64 B 32.04 - 33.56 C 31.45 - 34.15 D 31.19 - 34.41

D

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. A(47.788 - 49.212) B(47.865 - 49.135) C(45.806 - 51.194) D(47.722 - 49.278)

D

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. A 0.0793 B 01554 C 0.3446 D 0.4207 E 0.4483

D

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? A .0500 B .3520 C .9332 D .0668

D

Which of the following is advantage of a confidence interval estimate over a point estimate for a population parameter A. Interval estimates are more precise than point estimates B. Interval estimates are less accurate than point estimates C. Interval estimates are both more accurate and more precise than point estimates D. Interval estimates take into account the fact that the statistic being used to estimate the population parameter in a random variable

D

For a left tailed hypothesis test, the p value is the area under the normal curve A. That includes the test statistic "the tests data value B. To the right of the test statistics the tests data value C. That includes all possible values of z D. To the left of the test statistic " the tests data value"

D.

confidence interval

Estimate but instead of one value it's an interval of numbers

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. True or False

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. True or False

False

Smaller the standard error

More precise or better

Symmetric Populations

Require a smaller n then skewed population normally

Larger the N

Results in a smaller standard error

SDSM

Sample greater than or equal than 30

Central Limit Theorem

Sample size plus all possible sample means become approximately normal no matter what the samples population distribution is

Standard error

Sampling distribution of standard deviation

point estimate

Statistic "for a sample" that serves as a best guess of a population parameter "Sample mean is a point estimate for the population mean"

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 or False

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 or False

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 or False

True

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

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 or False

True

inferential statistics

Using sample data to make generalizations about an unknown population. "Sample data helps make an estimate of a population"

margin of error

Will change in size as we change our prescribed confidence level Changing the alpha value or amount of likelihood we allow type 1 error