BUS 205 Final Exam

Calculate the standard score of the given x value, x=88, where μ=88.6, σ=4.7 Round your answer to two decimal places.

-.13

Consider the following data. 13,6,−1,0,8,−11,6 Copy Data Step 1 of 3: Determine the mean of the given data. Step 2 of 3: Determine the median of the given data. Step 3 of 3: Determine if the data set is unimodal, bimodal, multimodal, or has no mode. Identify the mode(s), if any exist.

3 6 UNIMODAL 6

Calculate the interquartile range of the given data. 23,14,3,39,41,3,28,50,36,1,43,46,45,52,55

32

The mean of a probability distribution.

Expected Value

In a normal distribution the mean and median are equal to each other, but the mode is different.

FALSE

For the graph shown, determine which letter represents the mean, the median, and the mode. Letters may be used more than once. GRAPH GOES: A,C,B

Mean == A, Median == C, Mode == B

Determine whether the following events are mutually exclusive. Choosing a diamond or a spade out of a standard deck of cards.

Mutually Exclusive

Determine whether the following value could be a probability. −0.32

NO

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X≥4), n=8, p=0.4

.4059

The time spent waiting in the line is approximately normally distributed. The mean waiting time is 5 minutes and the variance of the waiting time is 9. Find the probability that a person will wait for more than 2 minutes. Round your answer to four decimal places.

.8413

Find the area under the standard normal curve between z=−2.81 and z=1.12. Round your answer to four decimal places, if necessary.

.8662

Suppose a large shipment of cameras contained 15% defectives. If a sample of size 232 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 7%? Round your answer to four decimal places.

.9972

Suppose a basketball player has made 265 out of 312 free throws. If the player makes the next 2 free throws, I will pay you $15. Otherwise you pay me $36. Step 1 of 2: Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values. Step 2 of 2: If you played this game 756 times how much would you expect to win or lose? Round your answer to two decimal places. Losses must be entered as negative.

0.79 597.24

Determine the value that can NOT be a probability. 0, 1.41, 70%, 5/6

1.4

In the long run, which plan has the higher payout?

A

A process whose trials have only two possible outcomes.

BIONOMIAL DISTRIBUTION

Select the three hypotheses that are incorrect.

Hypothesis B, E, H

Genders are an example of which type of data

NEITHER

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more Decimal place than the largest number of decimal places given in the data. 14,18,16,5,13,9,18,16,11,17

Range: 13 Population variance: 16.4, Population standard deviation: 4

he amount that is added to and subtracted from the point estimate to determine the confidence interval.

margin of error

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 30% of this population prefers the color brown. If 18 buyers are randomly selected, what is the probability that exactly 8 buyers would prefer brown? Round your answer to four decimal places.

0.0811

An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 342 watts with a standard deviation of 12 Watts. What is the probability that the mean amplifier output would be greater than 338.4 watts in a sample of 33 amplifiers if the claim is true? Round your answer to four decimal places.

0.9573

Step 1 of 5: What is the test statistic? Step 2 of 5: Is this a 1 or 2 tail test? Step 3 of 5: What is the p-value? Step 4 of 5: Should you accept or reject the null hypothesis? Step 5 of 5: If the level of significance was changed to 0.05, should the null hypothesis be accepted or rejected?

1.828 1-tail test 0.059 reject null hypothesis Accept the null hypothesis

Three cards are drawn with replacement from a standard deck. What is the probability that the first card will be a diamond, the second card will be a red card, and the third card will be an ace? Express your answer as a fraction or a decimal number rounded to four decimal places.

1/104

The electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. They would like the estimate to have a maximum error of 0.13 kWh. A previous study found that for an average family the variance is 1.69 kWh and the mean is 15.2 kWh per day. If they are using a 99% level of confidence, how large of a sample is required to estimate the mean usage of electricity? Round your answer up to the next integer.

664

Suppose that IQ scores have a bell-shaped distribution with a mean of 104 and a standard deviation of 18. Using the empirical rule, what percentage of IQ scores are between 86 and 122?

68%

Find the expected value E(X)E(X) of the following data. Round your answer to one decimal place.

9.2

A market research company wishes to know how many energy drinks teenagers drink each week. They want to construct a 95% confidence interval with an error of no more than 0.07. A consultant has informed them that a previous study found the mean to be 5.4energy drinks per week and found the variance to be 1.21 What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.

949

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.62 and a standard deviation of 0.39. Using the empirical rule, what percentage of the students have grade point averages that are between 1.84 and 3.4

95%

Decide if the following probability is classical, relative frequency, or subjective. Selecting a king from a standard deck of cards.

CLASSICAL PROBABILITY

Select the scenario which is an example of simple random sampling.

College administration wants to conduct a survey to determine the demand for an insurance program at the college. Students are selected randomly from the college and mailed a questionnaire.

Classify the following as either a discrete random variable or a continuous random variable. The actual volumes in 50 recently manufactured bottles of mineral water.

Continuous

A ______________________ sample size reduces the potential for extreme sampling error, there is no guarantee that a _________________ sample size will always give a __________________ sampling error.

LARGER LARGER SMALLER

When the entire alpha is located in one tail of the distribution, this is known as a ________________.

One-tailed test

If data is left skewed, than the mean is __________________ of the median

TO THE LEFT

An interval from sample values that can provide a range that will include the true population's parameter at a specified level of confidence.

confidence interval

The percentage of all possible confidence intervals that will contain the true population parameter.

confidence level

A characteristic of certain statistics in which the average of all possible values of the sample statistic equals a parameter.

Unbiased Estimator

A statement about a population parameter that will be assumed true during a test and will only be rejected with contradictory evidence.

null hypothesis

When the alpha level is split evenly between two tails of a distribution, this is known as a _________________.

two tailed test

Calculate the standard score of the given x value, x=35.6, where x‾=41, s=5.7. Round your answer to two decimal places.

−0.95

Suppose a basketball player has made 188 out of 376 free throws. If the player makes the next 3 free throws, I will pay you $23. Otherwise you pay me $4. Step 1 of 2: Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

-$0.63

Suppose a basketball player has made 188 out of 376 free throws. If the player makes the next 3 free throws, I will pay you $23. Otherwise you pay me $4$⁢. Step 2 of 2: If you played this game 994 times how much would you expect to win or lose? Round your answer to two decimal places. Losses must be entered as negative.

-$626.22

A box contains 1616 green marbles and 1515 white marbles. If the first marble chosen was a white marble, what is the probability of choosing, without replacement, another white marble? Express your answer as a fraction or a decimal number rounded to four decimal places.

7/15

The three logical operators that can be used in a null hypothesis.

=, ≤, ≥

Given the following weights and data values, calculate the mean. Round your answer to three decimal places.

Correct Answer:6.415

The mean can be drawn away from the median by _____________________________.

Extreme Values

A random sample will almost always be a perfect representation of the population.

FALSE

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 210 engines and the mean pressure was 5.0 pounds/square inch (psi). Assume the population standard deviation is 0.9. The engineer designed the valve such that it would produce a mean pressure of 4.9 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Make the decision to reject or fail to reject the null hypothesis.

Fail to Reject Null Hypothesis

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 5.3 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 9 samples is 5.6 ppm with a standard deviation of 0.6 Assume the population is normally distributed. A level of significance of 0.05 will be used. Make the decision to reject or fail to reject the null hypothesis.

Fail to Reject Null Hypothesis

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 250 engines and the mean pressure was 6.6 lbs/square inch. Assume the variance is known to be 1. If the valve was designed to produce a mean pressure of 6.5 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? State the null and alternative hypotheses for the above scenario.

H0: μ=6.5 Ha: μ≠6.5

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 447 gram setting. Is there sufficient evidence at the 0.1 level that the bags are overfilled? Assume the population is normally distributed. State the null and alternative hypotheses for the above scenario.

HO: u=447 HA>447

In the long run, which plan has the higher payout? Plan APayout $60,000$⁢60,0000.170.17$65,000$⁢65,0000.240.24$95,000$⁢95,0000.590.59 Plan BPayoutP(Payout)P(Payout)−$30,000−$⁢30,0000.110.11$20,000$⁢20,0000.30.3$80,000$⁢80,0000.59

PLAN A

The difference between a measure computed from a sample and the corresponding measure computed from the population.

Sampling Error

Decide if the following probability is classical, relative frequency, or subjective. You guess that there is a 35% chance that you will be assigned homework in your philosophy class on Thursday.

Subjective Probability

The number of independent values available to estimate the population's standard deviation.

degrees freedom

Right skewed data means that the tail of the data _____________________________.

extends to the right

Using traditional methods, it takes 9.1 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 22 students and observed that they had a mean of 8.9 hours with a variance of 1.96. A level of significance of 0.1 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.

−0.670

G0-For-Gold Fitness has two apps, a weight training app, and a marathon training app. Go-For-Gold uses the apps to sell fitness supplements as well as provide users with helpful information. Management would like to know if the in-app purchases per day generated by the apps are different. Assume .02 for the level of significance and variances are assumed equal. Using Excel Data Analysis determine the answers to the following questions. Step 1 of 4: What is the test statistic? Step 2 of 4: Is this a 1 or 2 tail test? Step 3 of 4: What is the p-value? Step 4 of 4: Should you accept or reject the null hypothesis?

−3.128 2-tail test 0.014 Reject null hypothesis

A market research company wishes to know how many energy drinks adults drink each week. They want to construct a 80% confidence interval with an error of no more than 0.08 A consultant has informed them that a previous study found the mean to be 7.9 energy drinks per week and found the variance to be 0.64 What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.

164

If p-value is higher than alpha, then you should ______________.

accept null hypothesis

The value related to alpha that leads to rejecting the null hypothesis.

critical value

Samples that are selected so that values in one sample are matched with the values in a second sample.

paired samples

Select the correct Matches:Group 1A. PopulationB. SampleC. Data measured in categoriesD. Data measured in numbersE. Data that can be ranked in order of relationshipF. Data that can be measured on a scale of equal distant pointsG. The lowest form of dataH. Finding important hidden relationships in dataGroup 21. Quantitative2. Interval3. Data Mining4. Parameters5. Qualitative6. Statistics7. Ordinal8. Nominal

A4, B6, C5, D1, E7, F2, G8, H3

A statement that includes all the population values not included in the null hypothesis and will be deemed true if the null hypothesis is rejected.

Alternate Hypothesis

Select the scenario which is an example of voluntary sampling.

An airline is interested in getting feedback about their on-board catering experience. They place a questionnaire in the pocket behind each airline seat for passengers to fill out.

The electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. Assume that the population standard deviation is 1.8 kWh. The mean electricity usage per family was found to be 15.8 kWh per day for a sample of 872 families. Construct the 98% confidence interval for the mean usage of electricity. Round your answers to one decimal place.

Lower endpoint: 15.7 Upper endpoint: 15.9

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X=3)), n=17, p=0.5

.0052

A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 83 minutes with a mean life of 541 minutes. If the claim is true, in a sample of 160 batteries, what is the probability that the mean battery life would be greater than 553.9 minutes? Round your answer to four decimal places.

.0246

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 14 Pennies 20 Dimes 14 Nickels 29 Quarters What is the probability that you reach into the jar and randomly grab a quarter and then, without replacement, a nickel? Express your answer as a fraction or a decimal number rounded to four decimal places.

.0694

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50% of this population prefers the color red. If 12 buyers are randomly selected, what is the probability that exactly a half of the buyers would prefer red? Round your answer to four decimal places.

.2255

A coin is tossed 6 times. What is the probability of getting all tails? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

0.0156

A pizza delivery company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 2001 customers. The data is summarized in the table below. What is the probability that a customer is male and lives with his parents? Express your answer as a fraction or a decimal number rounded to four decimal places.

0.0510

Consider the following data: −14,13,10,15,10,14−14,13,10,15,10,14 Step 1 of 3: Calculate the value of the sample variance. Round your answer to one decimal place. Step 2 of 3: Calculate the value of the sample standard deviation. Round your answer to one decimal place Step 3 of 3: Calculate the value of the range..

120.4 11.0 29

For every dataset the sum of deviations of the data from the mean is always _______________.

ZERO

A marketing research company desires to know the mean consumption of milk per week among males over age 25. A sample of 2213 males over age 25 was drawn and the mean milk consumption was 2.4liters. Assume that the population standard deviation is known to be 1.2 liters. Construct the 95% confidence interval for the mean consumption of milk among males over age 25 Round your answers to one decimal place.

low: 2.4 high: 2.5

A soft drink manufacturer wishes to know how many soft drinks adults drink each week. They want to construct a 85% confidence interval for the mean and are assuming that the population standard deviation for the number of soft drinks consumed each week is 1. The study found that for a sample of 467 adults the mean number of soft drinks consumed per week is 7.6 Construct the desired confidence interval. Round your answers to one decimal place.

low: 7.5 high: 7.7

A single statistic from a sample used to estimate a population.

point estimate

If the confidence level is decreased, the margin of error is ___________________________. If the confidence level is increased, the margin of error is ___________________.

reduced, increased