STATS PRACTICE EXAM 2

Find a 95% confidence interval for μ when n = 9, x-bar = 103.14 and s = 5.25. A. (99.10, 107.18) B. (99.71, 106.57) C. (101.39, 104.89) D. (101.79, 104.49)

A. (99.10, 107.18)

Fill in the blank: The t-distribution with 8 degrees of freedom has ____________________ the standard Normal distribution. A. the same center but is more spread out than B. the same center but is less spread out than C. the same center and spread as D. a different center and a different spread than

A. the same center but is more spread out than

t* s/√n

Margin of error for estimating μ

Standard error of x̄

S /√n

The mean weight for starting football players on a top 20 team in Division I was 105 kg in the 1988 football season. The question asked by a researcher was whether starters on non-top 20 teams weighed less than 105 kg on the average. Thirty six starting players on non-top 20 teams were randomly selected. What are the null and alternative hypotheses necessary to answer the question, "Is the mean weight for non-top 20 starters less than 105 kg?" a) H 0: μ = 105 versus Ha: μ < 105 b) H 0: μ = 105 versus Ha: μ > 105 c) H 0: μ = 105 versus Ha: μ ≠ 105 d) H 0 : x̄= 105 versus Ha: x̄< 105 e) H 0 : x̄= 105 versus Ha: x̄> 105 f) H 0 : x̄= 105 versus Ha: x̄≠ 105

a) H 0: μ = 105 versus Ha: μ < 105

The radius of a wheel on a toy car is supposed to be 3/4 of an inch. If the wheel is too small or too large, the car will not roll properly. The manufacturer measures the radius in a random sample of 20 cars to determine whether the mean radius of the wheels currently being produced is different from 3/4 of an inch. Select the correct null and alternative hypotheses for this test. a) H 0: μ = 3/4 in. versus Ha: μ ≠ 3/4 in. b) H 0: μ = 3/4 in. versus Ha: μ < 3/4 in. c) H 0: μ = 3/4 in. versus Ha: μ > 3/4 in. d) H 0 : x̄= 3/4 in. versus Ha: x̄≠ 3/4 in. e) H 0 : x̄= 3/4 in. versus Ha: x̄> 3/4 in. f) H 0 : x̄= 3/4 in. versus Ha: x̄< 3/4 in.

a) H 0: μ = 3/4 in. versus Ha: μ ≠ 3/4 in.

Which one of the following is NOT part of the definition for P -value? a) Probability that the null hypothesis is true. b) Probability of obtaining a value of the statistic. c) The value of the statistic is farther from the claimed parameter value than the observed statistic. d) The null hypothesis is assumed to be true.

a) Probability that the null hypothesis is true.

Suppose the P -value for the test described in the above question is 0.013 (although this is not the correct value.) What is the appropriate statistical conclusion at the .05 level of significance? a) Reject H 0 and conclude that the mean exceeds 6.3 times per month. b) Fail to reject H 0 and conclude that the mean exceeds 6.3 times per month. c) Reject H 0 and conclude that the mean does NOT exceed 6.3 times per month. d) Fail to reject H 0 and conclude that credit card usage has stayed the same at 6.3 times per month on the average.

a) Reject H 0 and conclude that the mean exceeds 6.3 times per month.

Which hypothesis is assumed to be true until evidence is found to disprove or contradict it? a) The null hypothesis. b) The alternative hypothesis. c) The claimed hypothesis. d) The significant hypothesis.

a) The null hypothesis.

In 1990, the average cost of a normal pregnancy and delivery was $4334. Data was collected recently on a random sample of 29 recent births in a particular state. A 90% confidence interval was computed to be ($4663, $4787). On the basis of this interval, can we say that the average cost in that particular state is different from the average cost of $4334? Why or why not? a) Yes, because $4,334 is outside the confidence interval. b) Yes, because the mean for the sample of 29 births is $4,725 and that is larger than $4,334. c) No, because $4,334 is a possible value for the parameter when the sample mean is $4,725. d) No, because a sample of 29 is not a large enough sample from which we can draw inferences.

a) Yes, because $4,334 is outside the confidence interval.

Twelve runners were randomly sampled and asked to run a 10-kilometer race. Their times are recorded in the following stemplot. On the basis of the following stemplot, is use of a one-sample t confidence interval procedure to estimate the mean time appropriate? Stem-and-leaf of runners' speeds n = 12 29 | 36 30 | 556 31 | 025 32 | 12 33 | 00 a) Yes, because the runners were randomly sampled and there are no serious outliers in the stem plot. b) Yes, because the population of runners times is normally distributed. c) No, because 12 runners is too few relative to the total number of runners in the world. d) No, because the sample size is too small for inference.

a) Yes, because the runners were randomly sampled and there are no serious outliers in the stem plot.

Lifetimes of a particular flashlight battery have a non-Normal distribution with mean, μ , of 35.6 hours and standard deviation σ = 5.4 hours. A quality inspector is planning to take a random sample of 43 of these batteries and compute the sample mean. Can he compute the probability that the sample mean will exceed 35.7 hours using the standard Normal table? Why or why not? a) Yes, because the sample will be large and random so the Central Limit Theorem applies. b) Yes, because the original population was normally distributed and sample will be random. c) No, because the sample size is too small to apply the Central Limit Theorem. d) No, because the original distribution was not normally distributed.

a) Yes, because the sample will be large and random so the Central Limit Theorem applies.

Which one of the following does NOT have variability? a) a parameter b) data c) a statistic d) a random variable e) a quantitative response variable

a) a parameter

Fill in the blank: For the sampling distribution of x̄ created by taking random samples from a left skewed population, the standard deviation of the sampling distribution of x̄ _______________ as n increases. a) decreases b) stays the same c) increases d) cannot be determined

a) decreases

Fill in the blank: The t-distribution with 4 degrees of freedom is _______________________ the standard Normal distribution. a) flatter and more spread out than b) taller and skinnier than c) the same as d) shaped the same as but has a different center than

a) flatter and more spread out than

The standard deviation of the sampling distribution of x̄ is _____________ the standard deviation of the population from which samples of size n >1 are taken to create the sampling distribution. a) less than b) equal to c) greater than d) not comparable with

a) less than

Whenever performing a one sample t procedure on means, we should check for a) randomization and no outliers in the data. b) random allocation of individuals to treatments. c) only randomization. d) randomization and whether we sampled enough of the population.

a) randomization and no outliers in the data.

Fill in the blank: Keeping all else constant, the sample mean of thirty measurements will have a margin of error that is ______________________ the margin of error for a sample mean of three measurements. a) smaller than b) equal to c) larger than

a) smaller than

Control charts are designed to sound an alarm when a) the amount of observed variation exceeds the amount that could be attributable to natural variation. b) variation is observed in the x'̄s. c) the observed sample means differ from the control standard by an amount attributable to natural variation. d) the sample mean, x,̄differs from the control standard by even a small amount.

a) the amount of observed variation exceeds the amount that could be attributable to natural variation.

Sample results are said to be statistically significant whenever a) the difference between the observed statistic and the claimed parameter value given in H 0 is too large to be due to chance. b) the difference between the true situation and the observed situation could plausibly have resulted because H 0 is false. c) the researcher subjectively classifies the observed deviation from what was expected under H 0 as large enough to matter. d) the difference between the observed statistic and the claimed parameter value is large enough to be worth reporting.

a) the difference between the observed statistic and the claimed parameter value given in H 0 is too large to be due to chance.

The value of a parameter will only change if a) the population changes. b) a different sample is obtained from the population. c) the sample size is increased. d) repeated samples are taken from the same population.

a) the population changes.

Tests of significance on μ and confidence intervals for μ (with σ known) are based on a) the sampling distribution of x̄ b) the shape of the population distribution c) the Law of Large Numbers d) the language of sample designs.

a) the sampling distribution of x̄

Fill in the blank: Central Limit Theorem allows us to compute probabilities on ___________ using the standard Normal table provided the sample size of the random sample is sufficiently large. a) x̄ b) μ c) s d) sample measurements.

a) x̄

Which one of the following is not a statistic? a) μ b) x̄ c) p̂ d) s e) median of data in a sample

a) μ

Referring to the above question and assuming that computing the probability is okay, what is the probability that the sample mean is below 35.7? a) 8786 b) 0.5478 c) 0.4522 d) 0.1214 e) 0.0185

b) 0.5478

Do you need to apply the Central Limit Theorem to compute the probability on the mean weight of 16 randomly selected bags described in the above question? a) No, because the individual was not randomly selected. b) No, because the distribution of weights is Normally distributed. c) Yes, because we used the standard Normal table. d) Yes, because the sample was random and n was large.

b) No, because the distribution of weights is Normally distributed.

How is level of confidence determined? a) From the confidence intervals. b) Subjectively determined by the researcher. c) The probability that the observed statistic falls in the confidence interval. d) Computed from margin of error. e) From the sample size: the larger the sample size, the larger the level of confidence.

b) Subjectively determined by the researcher.

The weekly oral dosage of anabolic steroids was measured on a sample of 20 body builders. A 95% confidence interval estimate for the average weekly oral dose of anabolic steroids obtained from these results was 152 mg to 194 mg. Which one of the following is a correct interpretation of this confidence interval? a) There is a .95 probability that the average weekly dose of anabolic steroids used by body builders is between 152 mg. and 194 mg. b) We are 95% confident that the average weekly dose of anabolic steroids used by all body builders is between 152 mg. and 194 mg. c) We are 95% confident that the average weekly dose of anabolic steroids used by the 20 body builders is between 152 mg. and 194 mg. d) 95% of the time, the average weekly dose of anabolic steroids used by body builders is between 152 mg. and 194 mg. e) 95% of all body builders use between 152 mg. and 194 mg. of anabolic steroids per week.

b) We are 95% confident that the average weekly dose of anabolic steroids used by all body builders is between 152 mg. and 194 mg.

The Central Limit Theorem on x̄ requires a) the sample size is greater than 10% of the population. b) a large random sample. c) Normality of the sampled population.

b) a large random sample.

If we fail to reject the null hypothesis, we could be making a) a type I error b) a type II error c) either a type I or a type II error d) no error. an error is only made when we accidentally reject the null hypothesis

b) a type II error

Fill in the blank: For the sampling distribution of x̄ created by taking random samples from a left skewed population, the shape is _______________ for large n. a) slightly skewed right b) approximately normal c) slightly skewed left d) exactly normal

b) approximately normal

For the a) Slightly right skewed sampling distribution of x̄described in question 11, what is its shape? b) Approximately Normal c) Slightly left skewed d) Cannot be determined because the shape of the population is unknown

b) approximately normal

The margin of error in a confidence interval covers only which kind of errors? a) interviewer errors b) chance errors due to random sampling c) bias errors due to wording of questions d) computational errors

b) chance errors due to random sampling

Suppose we are testing the hypothesis H0: μ = 850 versus the hypothesis Ha μ > 850. For a = 0.05 and P-value = .092, what decision should be made? a) reject H0 b) fail to reject H0 c) reject Ha d) fail to reject Ha e) Accept H0

b) fail to reject H0

The test statistic t = xˉ− μ / s√n measures a) the maximum distance between the observed x̄ and the claimed parameter value μ 0. b) how many standard errors the observed x̄ is from the claimed parameter value μ 0. c) the variability of the sample x 's about the claimed parameter value μ 0. d) the total number of standard deviations, or σ , units x is from the claimed parameter value μ 0.

b) how many standard errors the observed x̄ is from the claimed parameter value μ 0.

What two things do we need in order to compote margin of error for a one-sample t confidence interval for μ? a) sample size and level of confidence b) level of confidence and the standard error of x̄ c) values for μ and σ d) the mean and standard deviation of the sampling distribution of x̄

b) level of confidence and the standard error of x̄

Standard error of x̄ refers to a) the amount an observed statistic for x̄ differs from its parameter, μ. b) the estimate of the standard deviation of the sampling distribution of x.̄ c) the number of standard deviations that the observed statistic, x̄, differs from its parameter, μ. d) the maximum amount that a statistic, x̄, differs from its parameter, μ.

b) the estimate of the standard deviation of the sampling distribution of x.̄

A test of significance is intended to assess a) the evidence provided by data against the alternative hypothesis in favor of the null hypothesis. b) the evidence provided by data against the null hypothesis in favor of the alternative hypothesis. c) the probability that the null hypothesis is true. d) the probability that the alternative hypothesis is true.

b) the evidence provided by data against the null hypothesis in favor of the alternative hypothesis.

Margin of error for 99% confidence tells us a) how much the measurements deviate from the unknown parameter mean. b) the most a statistic differs from the parameter for the middle 99% of all possible statistic values. c) the difference between the observed statistic and the unknown parameter value. d) how many standard deviations the observed statistic is from the unknown parameter value.

b) the most a statistic differs from the parameter for the middle 99% of all possible statistic values.

Which one of the following measures the variability of a statistic? a) the standard deviation of the data. b) the standard deviation of the sampling distribution for the statistic. c) the total sum of squared deviations of the observations about the mean. d) the number of standard deviations that a statistic value differs from the parameter value.

b) the standard deviation of the sampling distribution for the statistic.

The theoretical sampling distribution of a statistic consists of a) the results of a sample. b) the values of a statistic from all possible samples. c) the range of the values in a sample. d) a set of sample data that has the same shape as the original population.

b) the values of a statistic from all possible samples.

The standard deviation of the sampling distribution of x̄ measures a) the variability of observations about the mean. b) the variability of the sample mean values about the parameter, μ. c) the height of the sampling distribution. d) the error or difference between the value of a statistic and its parameter.

b) the variability of the sample mean values about the parameter, μ.

We use a t-distribution with n-1 degrees of freedom rather than the standard normal distribution whenever a) the Central Limit Theorem does not apply. b) we are using s to estimate σ. c) the population is not normally distributed. d) we can apply the Law of Large numbers and do not need normality.

b) we are using s to estimate σ.

What is the difference between σ and s? a) there is no difference. b) σ is the standard deviation of a population whereas s is the standard deviation of a sample. c) σ measures where the data tend to center whereas s measures spread of data. d) σ is usually a known value whereas s has to be estimated from sample data.

b) σ is the standard deviation of a population whereas s is the standard deviation of a sample.

Suppose you are testing H 0: μ = 30 vs. H a: μ > 30 with a sample of size n = 19 and the test statistic is t = 1.92. What is the P -value? a) 0.0192 b) 0.0274 c) 0.025 < P-value < 0.05 d) 0.05 < P-value < 0.10

c) 0.025 < P-value < 0.05

For the theoretical sampling distribution of x̄ created by taking all possible samples of size 16 from a very left skewed population with μ = 22 and σ = 4, the mean of this sampling distribution... Referring to the sampling distribution of x̄ described in the question above, what is the standard deviation of the sampling distribution of x̄? a) 5.5 b) 4.0 c) 1.0 d) 0.25 e) 0.0625 f) cannot be determined

c) 1.0

Referring to the manufacturing process in question 14 above, what are the lower and upper limits for the control chart for x̄from samples of size 16? a) 13.8, 16.2 b) 14.9, 15.1 c) 14.8, 15.2 d) 11.4, 18.6

c) 14.8, 15.2

The manager of a major chain department store decided to offer a promotion to increase customers' usage of their credit cards issued by the chain. Before the promotion, credit card holders used their cards an average of 6.3 times per month. During the month of the promotion a random sample of 100 credit card holders used their cards an average of 6.8 times with a standard deviation of 2.5. For testing the hypotheses H 0: μ = 6.3 versus H a: μ > 6.3, what is the value of the standardized test statistic? a) 0.20 b) 0.50 c) 2.00 d) Impossible to determine from information given.

c) 2.00

A poultry farmer wishes to estimate the average incubation period (the number of days between a hen laying her egg and the time the egg hatches) for eggs on his farm. He plans to take a sample and make a 98% confidence interval, and would like a margin of error of half a day. It is known that the distribution of incubation lengths has a standard deviation of 1.5 days. How many eggs does he need to sample to create the desired interval? a) 6 b) 17 c) 49 d) 147

c) 49

How large of a sample should you need in order to have a margin of error of 2 with a 95% confidence level when the standard deviation is 30? a) 30 b) 864 c) 865 d) 3457

c) 865

Which one of the following is NOT a correct statement about margin of error? a) A small margin of error says that we have pinned down the parameter quite precisely. b) For fixed level of confidence, increasing the sample size, n, reduces the margin of error. c) For fixed sample size, decreasing level of confidence increases the margin of error. d) To obtain a smaller margin of error without increasing sample size, you must be willing to accept lower confidence.

c) For fixed sample size, decreasing level of confidence increases the margin of error.

What do we obtain from the sampling distribution of x̄, created assuming the null hypothesis is true, in order to perform a test of hypothesis? a) sample size b) level of significance or a c) P-value d) the value of x̄

c) P-value

Refer to the above question. Suppose x̄= 50.15 bushels per acre. Graphically, what represents the P -value? a) The area under the sampling distribution of x̄curve between 50 and 50.15. b) The area under the sampling distribution of x̄curve to the left of 50.15. c) The area under the sampling distribution of x̄curve to the right of 50.15. d) The probability that H 0 is true if x̄= 50.15.

c) The area under the sampling distribution of x̄curve to the right of 50.15.

Referring to question above, the mean of the sample is 173 mg and the margin of error for the confidence interval given in the above question is 21 mg. Which one of the following is a correct interpretation of margin of error? a) 95% of the time, 173 will differ from the true average weekly oral dose by 21 mg. b) The figure given as 173 is not the exact value; 173 may fluctuate anywhere between 152 and 194. c) The maximum difference we expect between our sample result and the true average weekly oral dose is no more than 21 mg. d) 95% of the time, the responses of all body builders will be within 21 mg of 173 mg.

c) The maximum difference we expect between our sample result and the true average weekly oral dose is no more than 21 mg.

A random sample of size 10 was taken from a population. The sample has a standard deviation of zero. Which of the following statements must be true. a) The population has a standard deviation of zero. b) The sample mean is greater than the sample median. c) The ten data points in the sample are all equal in numerical value. d) The sample size is too small to compute standard deviation.

c) The ten data points in the sample are all equal in numerical value.

Suppose you are testing the following hypotheses. What is the type I error for these hypotheses? H 0: Cake is not done, versus H a: Cake is done a) To believe that the cake is not done when it is still not done. b) To believe that the cake is not done when it really is done. c) To believe that the cake is done when it is still not done. d) To believe that the cake is done when it really is done.

c) To believe that the cake is done when it is still not done.

For the theoretical sampling distribution of x̄ created by taking all possible samples of size 16 from a very left skewed population with μ = 22 and σ = 4, the mean of this sampling distribution a) is approximately equal to 22. b) is slightly less than 22. c) is exactly equal to 22. d) is slightly greater than 22. e) would approach 22 if the sample size were to continually increase.

c) is exactly equal to 22.

The null hypothesis is a statement of a) the many possible values of the statistic. b) how well the statistic estimates the parameter to be tested. c) no effect or no change in the population parameter. d) an estimate of a population parameter.

c) no effect or no change in the population parameter.

For the theoretical sampling distribution of x̄ created by taking all possible samples of size 16 from a very left skewed population with μ = 22 and σ = 4, the mean of this sampling distribution... Referring to the sampling distribution of x̄ described in the question above, what is its shape? a) slightly right skewed b) approximately normal c) slightly left skewed d) cannot be determined because the shape of the population is unknown

c) slightly left skewed

42. When using a confidence interval to perform a two-sided test, H 0 will be rejected whenever a) the claimed parameter value in H 0 falls inside the confidence interval. b) the observed statistic value from the sample falls inside the confidence interval. c) the claimed parameter value in H 0 falls outside the confidence interval. d) the observed statistic value from the sample falls outside the confidence interval.

c) the claimed parameter value in H 0 falls outside the confidence interval.

What is the purpose of a confidence interval? a) to measure the amount of confidence you have in your interval b) to determine the percentage of times the parameter will fall into your interval c) to estimate the value of a parameter d) to give a range of reasonable probability simulations

c) to estimate the value of a parameter

The time it takes college freshman to complete the Mason Basic Reasoning Test is normally distributed with a mean of 24 minutes and a standard deviation of 5 minutes. What symbol should be used to represent the mean of 24 minutes? a) σ b) s c) μ d) x̄

c) μ

Which of the following is NOT one of the conditions for using the formula xˉ ± t* s ? √n a) Data must be random. b) We must be able to compute the mean and standard deviation from sample data. c) σ, the standard deviation of the population, must be known d) The population distribution is Normally distributed.

c) σ, the standard deviation of the population, must be known

Referring to the sampling distribution of x̄described in question 11, what is the standard deviation of the sampling distribution of x?̄ a) 5.5 b) 4.0 c) 1.0 d) 0.25 e) 0.0625 f) Cannot be determined

c. 1sigma/square root of n4/4 = 1

Suppose we have H 0: μ = 30 versus H a: μ > 30 with P-value = .032. If we decided to test H 0: μ = 30 versus H a: μ ≠ 30, what is the P -value for this new H a assuming all other factors are the same? a) .016 b) .032 c) .050 d) .064

d) .064

Suppose we were to test the hypotheses H0: µ = 80 versus Ha : µ < 80 and computed the standardized value of the test statistic to be t = -2.67 from the sample results of a sample of size n = 22. Using the t table, what is the P-value? a) 0.025 < P < 0.05 b) 0.02 < P < 0.025 c) 0.01 < P < 0.02 d) 0.005 < P < 0.01 e) cannot find using the t table since the t test statistic value is negative.

d) 0.005 < P < 0.01

Calculate the margin of error from a random sample of 27 pigs with a mean weight of 54.3 kg and a standard deviation s = 6.2 kg. Use 95% confidence. a) 0.22 kg. b) 0.45 kg. c) 1.13 kg. d) 2.45 kg. e) 21.48 kg.

d) 2.45 kg.

On a control chart, under what circumstance is the process out of control? a) A run of 9 consecutive sample means above the centerline or below the centerline b) A sample mean below the lower limit c) A sample mean above the upper limit d) All of the above e) None of the above

d) All of the above

We want to test the hypotheses H 0: μ = 50 versus H a: μ > 50 to determine whether a new variety of corn will yield more than 50 bushels per acre. We plan to sample 100 plots and measure yield per acre on each plot. Assuming H 0 is true and that σ = 5, describe the sampling distribution of x.̄ a) Right skewed. b) Standard normal. c) Approximately normal with mean 50 and standard deviation 5. d) Approximately normal with mean 50 and standard deviation 0.5. e) Unknown because we do not know the shape of the distribution of yield of corn.

d) Approximately normal with mean 50 and standard deviation 0.5.

All of the following are true statements about the P-value except one. Which statement is false? a) P-value is the area in the tail of the sampling distribution defined by H0 b) the smaller the P-value, the greater the evidence for the alternative hypothesis c) the larger the P-value, the greater the agreement between the data and H0 d) P-value is used to determine the significance level

d) P-value is used to determine the significance level

Which one of the following is a correct interpretation of the P -value given above in question 63? a) The probability that the null hypothesis is true is .013. b) The probability of rejecting a true null hypothesis is .013. c) The probability of obtaining a sample mean that exceeds the claimed mean value of 6.2 is .013. d) The probability of obtaining a sample mean that is as far or farther from the hypothesized mean value of 6.3 as the observed value of 6.8 is .013. e) The probability of getting a sample mean that is no more than 6.8 when the population mean is really 6.3 is .013.

d) The probability of obtaining a sample mean that is as far or farther from the hypothesized mean value of 6.3 as the observed value of 6.8 is .013.

Which one of the following is NOT synonymous with "Reject H 0" ? a) Results are statistically significant. b) P-value < α. c) Conclude Ha is correct. d) The results are due to chance.

d) The results are due to chance.

Which one of the following does NOT affect margin of error for a one-sample t confidence interval for μ? (Assume that the necessary conditions are met.) a) Level of confidence b) Sample size c) Standard error of x̄ d) Value of the parameter μ.

d) Value of the parameter μ.

The sampling distribution of a statistic has the following: a) shape. b) center. c) spread. d) all of the above.

d) all of the above.

What does significant in the statistical sense mean? a) no difference b) of great importance c) that the test statistic supports the null hypothesis d) not likely to happen just by chance if H0 were true

d) not likely to happen just by chance if H0 were true

The purpose of a confidence interval is to provide a) information about the range of data in a distribution. b) a measure of the confidence we can have in our sample results representing the population. c) a list of all possible values of the statistic from all possible samples. d) plausible values that a parameter could be.

d) plausible values that a parameter could be.

Level of confidence can be defined as a) the probability that a computed confidence interval contains the unknown parameter value. b) the percentage of time that the observations or measurements fall in the confidence interval. c) the probability that the observed statistic is in the confidence interval. d) the percentage of the time that the procedure will produce intervals that contains the parameter value.

d) the percentage of the time that the procedure will produce intervals that contains the parameter value.

Which one of the following is NOT a parameter? a) the mean of the measurements on all the individuals in a population. b) the proportion of a population that have a certain characteristic. c) the standard deviation of an entire population. d) the proportion in a sample survey that favor a certain opinion.

d) the proportion in a sample survey that favor a certain opinion.

What is the random variable of the sampling distribution of x?̄ a) the parameter being estimated b) the response variable c) the observations in the sample d) the sample mean

d) the sample mean

A manufacturing process produces potato chip bags that have Normally distributed weights, with a mean weight of 15 oz. and a standard deviation of .3 oz. What is the probability that 16 randomly selected bags have a mean weight that exceeds 15.2 oz? a) 0.9772 b) 0.9962 c) 0.5793 d) 0.5000 e) 0.0038 f) 0.0228

e) 0.0038

The mean score of the fourth exam in a statistics class with 1800 students at a large university was 79 with a standard deviation of 14. Suppose twenty-five students are to be randomly selected and their sample mean computed. What will be the mean and standard deviation of the sampling distribution of x?̄ a) 3.16, 0.56 b) 15.8, 0.56 c) 15.8, 2.8 d) 79.0, 14 e) 79.0, 2.8

e) 79.0, 2.8

Studies have shown the average life span of an adult male in the United States is 78 years. A sociologist believes that the average life span of an adult male in the state of Utah to be slightly higher. What hypotheses should he test? a) H 0 : x̄= 78 vs. Ha: x̄≠ 78 b) H 0 : x̄= 78 vs. Ha: x̄< 78 c) H 0 : x̄= 78 vs. Ha: x̄> 78 d) H 0: μ = 78 vs. Ha: μ ≠ 78 e) H 0: μ = 78 vs. Ha: μ > 78 f) H 0: μ = 78 vs. Ha: μ < 78

e) H 0: μ = 78 vs. Ha: μ > 78

Statistically significant is equivalent to all of the following except one. Which one is not equivalent? a) P-value < α. b) The difference between the observed value of the statistic and the value of the parameter as given in H 0 is too large to attribute to just chance variation. c) The probability of obtaining a sample statistic as extreme or more extreme than actually observed if H 0 were true is too small for us to believe that H 0 is correct. d) The observed statistic is inconsistent with the null hypothesis. e) The difference between an observed statistic and the true parameter value is due to chance variation.

e) The difference between an observed statistic and the true parameter value is due to chance variation

The Central Limit Theorem tells us that under certain conditions a) the shape of the histogram of the sample data will have the same shape as the population from which the sample was taken. b) the mean and standard deviation of the sample will be approximately equal to the mean and standard deviation of the population from which we sample. c) the shape of the population from which we sample will be approximately Normal. d) the shape of the data in the sample will be approximately Normal. e) the shape of the sampling distribution of x̄ will be approximately Normal.

e) the shape of the sampling distribution of x̄ will be approximately Normal.

The average time required to assemble a gas barbeque grill has been one hour and twenty minutes (80 minutes). An employee for the company has an idea that she thinks will shorten the time required for assembly. What hypotheses should be tested to determine whether her idea works? a) H 0 : x̄= 80 vs. Ha: x̄≠ 80 b) H 0 : x̄= 80 vs. Ha: x̄< 80 c) H 0 : x̄= 80 vs. Ha: x̄> 80 d) H 0: μ = 80 vs. Ha: μ ≠ 80 e) H 0: μ = 80 vs. Ha: μ > 80 f) H 0: μ = 80 vs. Ha: μ < 80

f) H 0: μ = 80 vs. Ha: μ < 80

true or false The shape of the histogram of sample data gets closer to the shape of the Normal distribution as the sample size increases.

false

true or false The shape of the histogram of sample data gets closer to the shape of the population as the sample size increases.

false

true or false The shape of the theoretical sampling distribution of x̄ is always Normal.

false

true or false The value of a sample statistic usually equals the value of the parameter of the population from which the sample was taken.

false

true or false 95% of all possible x'̄s will be within 2σ of μ.

false

true or false The mean of the theoretical sampling distribution of x̄ gets closer to μ as n increases.

false

σ

is the standard deviation of a population

s

is the standard deviation of a sample

α

level of significance or probability of making a type I error

x̄

mean of a sample

μ

mean of population or mean of the sampling distribution of x̄

β

probability of making a type II error

n

sample size

true or false The standard deviation of x̄ (for n > 1) is always less than the standard deviation of the population.

true

true or false Probabilities on individuals can only be computed using the standard Normal table if the population is Normally distributed.

true

true or false The standard deviation of x̄ is computed using σ / √n

true

true or false statistic varies because each random sample yields a different value for the statistic.

true

true or false x̄ gets closer and closer to μ as n increases.

true

Standard deviation of the sampling distribution of x̄

σ / √n