ST-370

For a given data set, the confidence interval will be wider for 95% confidence than for 90% confidence. a. True b. False

True

If a test rejects Ho: µ1 = µ2, then the confidence interval for (µ1 - µ2) having the same error probability does not contain zero. a. True b. False

True

If we decrease the confidence coefficient for a fixed n, we decrease the width of the confidence interval. a. True b. False

True

If σ is known, use the z test for μ. The population must be normally distributed if n < 30. a. True b. False

True

In a hypothesis test, the p value is 0.043. This means that the null hypothesis would be rejected at α = 0.05. a. True b. False

True

Regardless of the degrees of freedom, every t distribution is symmetric around 0. a. True b. False

True

A sampling distribution is a distribution for a statistic a. True b. False

True

As the sample size increases, the t distribution approaches to the standard normal distribution. a. True b. False

True

. There is no difference between testing a single population mean and testing the difference between two population means. a. True b. False

False

A hypothesis test is significant when the P-value is greater than β (P(type II error). a. True b. False

False

A pharmacist states that a 95% confidence interval for the average price of a particular prescription drug based on a sample of size 100 is $30.50 to $35.50. When asked to explain the meaning of this, the pharmacist says, "the probability that the true average price is between $30.50 and $35.50 is 95%." Is this statement correct? a. True b. False

False

Confidence intervals are useful when trying to estimate unknown statistics a. True b. False

False

For a continuous random variable number of outcomes are countable a. True b. False

False

For a given level of significance, increasing the sample size will always decrease the probability of committing a Type I error. a. True b. False

False

For hypothesis tests, the alternative hypothesis always includes the statement of equality between the parameter and the null value. a. True b. False

False

Given a sample mean of 2.1 and a population standard deviation of 0.7 from a sample of 10 data points, a 90% confidence interval will have a width of 2.36. a. True b. False

False

If the calculated value of the test t statistics is negative, then there is strong evidence that the null hypothesis is false. a. True b. False

False

The goal of the hypothesis test is to prove the null hypothesis a. True b. False

False

The null hypothesis is the proposition we want to find evidence for in a hypothesis testing. a. True b. False

False

The standard error of the mean increases as the sample size increases. a. True b. False

False

When the population is normal, we can always use a Z-test a. True b. False

False

A point estimator is called unbiased if the expected value of the point estimator is equal to the true population parameter. a. True b. False

True

A random sample of 20 observations produced a sample mean of x̅ = 92.4 and s = 25.8. The value of the standard error of x̅ is 5.8. a. True b. False

True

. If p-value of the test statistic is smaller than α, conclude 'Reject Ho'. a. True b. False

True

. If σ is unknown and n < 30, use the t test for testing μ. The population must be approximately normally distributed. a. True b. False

True

A 95% confidence interval for the mean reading achievement score for a population of third grades is (44.2, 54.2). The width of this interval is 10 a. True b. False

True

A confidence interval is a specific interval estimate of a parameter determined by using data obtained from a sample and by using the specific confidence level of the estimate. a. True b. False

True

A point estimate consists of a single sample statistic that is used to estimate the true population parameter. a. True b. False

True

Suppose an experiment and a sample size are fixed and a test statistic is chosen. Then, decreasing the size of the rejection region to obtain a smaller α value results in a larger β value for any parameter value consistent with Ha. a. True b. False

True

The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter. a. True b. False

True

The sample mean is a point estimate of the population mean. a. True b. False

True

The sample mean is an unbiased estimator for the population mean. a. True b. False

True

The sample proportion is an unbiased estimator of the population proportion. a. True b. False

True

The sampling method is independent when the individuals selected for one sample do not dictate which individuals are to be in a second sample. a. True b. False

True

The t critical value for 90% CI for df = 24 is 1.711 a. True b. False

True

The t distribution approaches the standardized normal distribution when the number of degrees of freedom increases. a. True b. False

True

The t distribution is more dispersed than the normal. a. True b. False

True

The t distribution is used to construct confidence intervals for the population mean when the population standard deviation(𝞂) is unknown. a. True b. False

True

The variance of the number of successes in a binomial experiment of n trials is σ 2 = n p (1 - p). a. True b. False

True

To perform inference on the difference of two population means, we must first determine whether the data come from an independent or dependent sample. a. True b. False

True

You are given a confidence interval for the population mean(µ) is 26 to 42. The sample mean used the construct this confidence interval was 34. a. True b. False

True

You buy a package of 122 Smarties and 19 of them are red.The value of the standard error of true proportion of red Smarties is 0.033. a. True b. False

True

The standard deviation of a point estimator is called the a. standard deviation b. point estimator c. variance of estimation d. standard error

d

A 95% confidence interval for a population mean (μ) is determined to be 100 to 120. If the confidence coefficient is reduced to 0.90, the interval for mu a. becomes narrower b. becomes wider c. does not change d. becomes 0.1

a

A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is known that the standard deviation of the population is 22 mph. Refer to Exhibit 2. The standard error of the mean is a. 2.00 b. 96.60 c. 4.24 d. 22.00

a

For the interval estimation of mu when sigma is known, the proper distribution to use is a. the standard normal distribution b. the t distribution with n degrees of freedom c. the t distribution with n + 1 degrees of freedom d. the t distribution with n + 2 degrees of freedom

a

In general, higher confidence levels provide a. wider confidence intervals b. narrower confidence intervals c. a smaller standard error d. unbiased estimates

a

The following random sample from a population whose values were normally distributed was collected. 10 8 11 11 The 95% confidence interval for μ is a. 7.75 to 12.25 b. 8.52 to 10.98 c. 8.00 to 10.00 d. 9.75 to 10.75

a

You compute a 95% confidence interval and a 99% confidence interval for a given data. Which of the following statement is correct? a. The 99% interval is wider b. You cannot be determined which interval is wider unless you know n and s c. The intervals have the same width d. The 95 % interval is wider

a

The z critical value ( z-cv) for a 97.8% confidence interval estimation is a. 2.02 b. 1.96 c. 2.00 d. 2.29

d

A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would be defective. With a 0.95 confidence, the sample size that needs to be taken if the desired margin of error is 0.04 or less is a. 216 b. 217 c. 111 d. 110

b

An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the a. confidence level b. interval estimate c. parameter value d. population estimate

b

As the sample size increases, the margin of error a. increases b. decreases c. stays the same d. increases or decreases depending on the size of the mean

b

Exhibit 1: In order to estimate the average time spent (μ) on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one week period. Assume the population standard deviation (σ) is 1.8 hours. Refer to Exhibit 1. If the sample mean is 9 hours, then the 95% confidence interval is a. 7.36 to 10.64 hours b. 8.61 to 9.39 hours c. 7.04 to 10.96 hours d. 7.80 to 10.20 hours

b

Exhibit 1: In order to estimate the average time spent (μ) on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one week period. Assume the population standard deviation (σ) is 1.8 hours. Refer to Exhibit 1. With a 0.95 probability, the margin of error is approximately a. 1.96 b. 0.39 c. 0.20 d. 1.64

b

The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the a. confidence level b. margin of error c. parameter estimates d. interval estimate

b

When "S" is used to estimate "σ", the margin of error is computed by using a. the mean of the population b. t distribution c. normal distribution d. the mean of the sample

b

Exhibit 1: In order to estimate the average time spent (μ) on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one week period. Assume the population standard deviation (σ) is 1.8 hours. Refer to Exhibit 1. The standard error of the mean is a. 7.50 b. 2.00 c. 0.20 d. 0.39

c

If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient (1-α) would be a. 0.1 b. 0.95 c. 0.9 d. 0.05

c

In developing an interval estimate, if the population standard deviation (σ) is unknown a. it is impossible to develop an interval estimate b. the standard deviation is arrived at using the range c. the sample standard deviation (S) can be used to estimate (σ) d. it is assumed that the population standard deviation is 1

c

The first percentile of student's distribution with 24 degrees of freedom is: a. 2.49 b. -2.50 c. -2.49 d. -2.80

c

The sample size needed to provide a margin of error of 2 or less with a 0.95 confidence when the population standard deviation equals 11 is a. 114 b. 100 c. 117 d. 111

c

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100? a. n = 20 b. n = 385 c. n = 40 d. n = 1537

d

An interval estimate is a range of values used to estimate a. the shape of the population's distribution b. the sampling distribution c. a sample statistic d. a population parameter

d

Exhibit 2: A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is known that the standard deviation of the population is 22 mph. Refer to Exhibit 2. If we are interested in determining an interval estimate for μ at 96.6% confidence, the Z critical value (z-cv) to use is a. 1.645 b. 1.96 c. 0.483 d. 2.12

d

Survey was taken of 588 residents in a county. The residents sampled were asked whether they think their local government did a good job overall. 490 responded "yes". Let p denote the proportion of all residents in that county who think their local government did a good job. Construct a 95% confidence interval for p. Round off to two decimal places. a. (0.68, 0.92) b. (489.97, 490.03) c. (0.10, 1.56) d.(0.80, 0.86) e. (0.79, 0.87)

d

The sample statistic "s" is the point estimator of a. p hat b. μ c. x bar d. σ

d