BAN 122: Updated PQ for Test 1

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-3. What is the minimum weight of the middle 95% of the players? a. 196 b. 151 c. 249 d. None of the alternative answers is correct.

1-.95=.05 .05/2=.025 1-.025= .975 .975 = z-score of 1.96 z-score is -1.96 = .025 -1.96= x-200/25 x = 151

How to find the Z in margin of error formula

1-probability= X/2 1- x = y Find Z score of y

A continuous random variable may assume a. all values in an interval or collection of intervals b. only integer values in an interval or collection of intervals c. only fractional values in an interval or collection of intervals d. all the positive integer values in an interval

A

A normal probability distribution a. is a continuous probability distribution b. is a discrete probability distribution c. can be either continuous or discrete d. always has a standard deviation of 1

A

A numerical measure from a sample, such as a sample mean, is known as a. a statistic b. a parameter c. the mean deviation d. the central limit theorem

A

A population where each element of the population is assigned to one and only one of several classes or categories is a a. multinomial population b. Poisson population c. normal population d. None of these alternatives is correct.

A

A sample statistic, such as x bar, that estimates the value of the corresponding population parameter is known as a a. point estimator b. parameter c. population parameter d. Both a parameter and a population parameter are correct.

A

If the variance of a data set is correctly computed with the formula using n 1 in the denominator, which of the following is true? a. the data set is a sample b. the data set is a population c. the data set could be either a sample or a population d. the data set is from a census

A

In a standard normal distribution, the range of values of z is from a. minus infinity to infinity b. -1 to 1 c. 0 to 1 d. -3.09 to 3.09

A

In the hypothesis testing procedure, a is a. the level of significance b. the critical value c. the confidence level d. level of significance

A

The sampling distribution of the sample mean a. is the probability distribution showing all possible values of the sample mean b. is used as a point estimator of the population mean c. is an unbiased estimator d. shows the distribution of all possible values of

A

The variance of the sample a. can never be negative b. can be negative c. cannot be zero d. cannot be less than one

A

The weight of an object, measured in grams, is an example of a. a continuous random variable b. a discrete random variable c. either a continuous or a discrete random variable, depending on the weight of the object d. either a continuous or a discrete random variable depending on the units of measurement

A

When the p-value is used for hypothesis testing, the null hypothesis is rejected if a. p-value < a b. a < p-value c. p-value > a d. p-value = z

A

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the mean from that sample will be between 183 and 186 is a. 0.1359 b. 0.8185 c. 0.3413 d. 0.4772

A 24/sqrt(64)= 3 s. std dev = 3 mean = 180 (186-180)/3= 2 (183-180)/3= 1 P(1 < z < 2) = .1587 - .0228 = .1359

A goodness of fit test is always conducted as a a. lower-tail test b. upper-tail test c. middle test d. None of these alternatives is correct.

B

A standard normal distribution is a normal distribution with a. a mean of 1 and a standard deviation of 0 b. a mean of 0 and a standard deviation of 1 c. any mean and a standard deviation of 1 d. any mean and any standard deviation

B

An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a a. discrete random variable b. continuous random variable c. complex random variable d. None of the answers is correct.

B

The absolute value of the difference between the point estimate, such as the sample mean, and the value of the population parameter it estimates, such as the population mean, is known as the a. confidence level b. sampling error c. parameter estimate d. interval estimate

B

The probability distribution of all possible values of the sample mean is called the a. central probability distribution b. sampling distribution of the sample mean c. random variation d. standard error

B

The process of analyzing sample data in order to draw conclusions about the characteristics of a population is called a. descriptive statistics b. statistical inference c. data analysis d. data summarization

B

The sampling error is the a. same as the standard error b. absolute value of the difference between an unbiased point estimate and the corresponding population parameter c. error caused by selecting a bad sample d. standard deviation multiplied by the sample size

B

The standard deviation of all possible xbar values is called the a. standard error of proportion b. standard error of the mean c. mean deviation d. central variation

B

Variations in process output that are due to factors such as machine tools wearing out are a. common causes b. assignable causes c. control causes d. None of these alternatives is correct.

B

A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is a. 15.2 to 24.8 b. 19.2 to 20.8 c. 19.216 to 20.784 d. 21.2 to 22.8

B 1-.9544= .0456 0.456/2 = 0.0228 1-.0228 = .9772 Z-score for .9772 was 2.00 Margin of error= 4.8/sqrt(144)=.4 20+2.00(.4) = 20.8 20-2.00(.4) = 19.2

A group of items such as incoming shipments of raw material is called a(n) a. sample plan b. incoming control c. lot d. None of these alternatives is correct.

C

A numerical measure computed from a sample, such as sample mean, is known as a a. population parameter b. sample parameter c. sample statistic d. population mean

C

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a a. contingency test b. probability test c. goodness of fit test d. None of these alternatives is correct.

C

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the a. approximation theorem b. normal probability theorem c. central limit theorem d. central normality theorem

C

If the lower-control limit of a P chart is negative, a. a mistake has been made in the computations b. use the absolute value of the lower limit c. it is set to zero d. None of these alternatives is correct.

C

The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is a. n-1 b. K-1 c. number of rows minus 1 times number of columns minus 1 d. a chi-square distribution is not used

C

The sample variance a. is always smaller than the true value of the population variance b. is always larger than the true value of the population variance c. could be smaller, equal to, or larger than the true value of the population variance d. can never be zero

C

Which of the following does not need to be known in order to compute the p-value? a. knowledge of whether the test is one-tailed or two-tailed b. the value of the test statistic c. the level of significance d. All of these are needed.

C

115. If a hypothesis is rejected at a 5% level of significance, it a. will always be rejected at the 1% level b. will always be accepted at the 1% level c. will never be tested at the 1% level d. may be rejected or not rejected at the 1% level

D

A probability distribution for all possible values of a sample statistic is known as a a. sample statistic b. parameter c. simple random sample d. sampling distribution

D

A single numerical value used as an estimate of a population parameter is known as a. a parameter b. a population parameter c. both a parameter or a population parameter are correct d. a point estimate

D

An important application of the chi-square distribution is a. making inferences about a single population variance b. testing for goodness of fit c. testing for the independence of two variables d. All of these alternatives are correct.

D

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

D

Which of the following is not a characteristic of the normal probability distribution? a. The mean, median, and the mode are equal b. The mean of the distribution can be negative, zero, or positive c. The distribution is symmetrical d. The standard deviation must be 1

D

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the mean from that sample will be larger than 82 is a. 0.5228 b. 0.9772 c. 0.4772 d. 0.0228

D 7/sqrt(49) = 7/7=1 S. Std. Dev = 1 Mean = 80 (82-80)/1= 2 = Z-score of 0.9772 1-0.9772 = 0.0228

65. The mean of a standard normal probability distribution a. is always equal to 1 b. can be any value as long as it is positive c. can be any value d. None of the alternative answers is correct.

D it is zero

P Value

Find the Test Statistic and look up the probability on the z-score chart. 1-x = p value

Chi Square Problems Reject if

Reject if x^2 (test statistic) > critical value from chi-chart Reject if p < a

Test statistic for Chi Square Problems

Sum of all the (O-E)^2/E

For one tail Test and two tail test, how do you find the critical value?

Use T chart df= k-1

Test Statistic

Use Z or T formula to Solve. USE FORMULA WITH x BAR

If sigma is unknown

Use t formula for test statistic

If sigma is known

Use z formula for test statistic

The uniform probability distribution is used with a. a continuous random variable b. a discrete random variable c. a normally distributed random variable d. any random variable

a. a continuous random variable

discrete random variable

can only take a countable number of values.

UCL

population mean + 3 * (Population std. dev)/sqrt(n) Mu + 3(sigma/sqrt(n))

p

proportion of non-conforming values 1-percent in decimal form

Random Variable

said to be random if the sum of the probabilities is one.

continuous random variable

where the data can take infinitely many values