STA2023 Final Exam Review

TCC STA2023 Final Exam Review

K Washington

Unit Three: Statistical Inference

Modules 7-9

Main Ideas

• Find probabilities for sampling distributions of means and proportions

• Conduct a hypothesis test for means and proportions

• Calculate/interpret confidence intervals for means and proportions

• Measurement/sampling biases

• Identify statistics, samples, parameters, and populations

Multiple Choice

If the p-value is less than α, we reject H₀

• True

• False

Multiple Choice

At a particular college, 78% of all students are receiving some kind of financial aid.The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving some sort of financial aid. Which of the following is true?

• A. 78% is a population and 72% is a sample.

• B. 72% is a population and 78% is a sample

• C. 78% is a parameter and 72% is a statistic

• D. 72% is a parameter and 78% is a statistic

Multiple Choice

These symbols represent the mean and standard deviation for which of the following distributions?

• A. The Population

• B. The Sample

• C. The Sampling Distribution

• D. Neither

Multiple Choice

The mean and standard deviation of a population are 200 and 20, respectively.

What is the probability of selecting 64 data values with a mean between 195 and 200?

• A. 41%%

• B. 48%

• C. 1.5%

• D. 0.5%

Multiple Choice

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25.

What is the standard error of the sampling distribution?

• A. 200

• B. 16

• C. 25

• D. 4

Multiple Choice

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25.

What is the mean of the sampling distribution?

• A. 200

• B. 16

• C. 25

• D. 4

Multiple Choice

A study found that in a sample of 44 subjects, 9 of agree that children under 6 shouldn’t be taken to nice restaurants.

The 95% confidence interval for p is (0.082, 0.318). Interpret this interval.

• A. 95% of the time the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8%.

• B. The population proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

• C. The probability that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8% is 95%.

• D. Based on this sample, I am 95% confident that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

Multiple Choice

If the 95% Confidence Interval for a population mean is (114.56, 125.54), then is it likely that the true population mean µ is greater than 130?

• A. Yes

• B. No

• C. Not enough information

• D. I have no idea what you're asking of me

Multiple Choice

A sample size of n = 64 is drawn from a population whose standard deviation is σ = 5.6.

Find the margin of error for a 99% confidence interval for µ.

• A. 1.799

• B. 1.798

• C. 1.803

• D. Not enough information

Multiple Choice

There is a law in ND saying that the ratio of elementary students to teachers can be no more than 22:1. A hypothesis test is performed to determine if the proportion of schools is above 25% using an SRS of 85 schools. At the 0.05 significance level, what conclusion can be made if 32 of the schools surveyed exceed this ratio?

• A. Since the p-value is less than the level of significance level, the null hypothesis should be rejected. There is significant evidence that the true proportion of schools with a higher ratio of more than 25%.

• B. Since the p-value is greater than the level of significance level, the null hypothesis should be rejected. There is significant evidence that the true proportion of schools with a higher ratio of more than 25%.

• C. Since the p-value is less than the level of significance level, the null hypothesis should not be rejected. There is not significant evidence that the true proportion of schools with a higher ratio of more than 25%.

• D. Since p-hat = 0.376 > 0.05, the null hypothesis should not be rejected. There is not significant evidence that the true proportion of schools with a higher ratio is greater than 25%.

• E. Since p-hat = 0.376 > 0.05, the null hypothesis should be rejected. There is significant evidence that the true proportion of schools with a higher ratio is greater than 25%.

Multiple Choice

Conduct a test to determine whether or not the population proportion of voters in favor of proposal A is greater than 50%. In a random sample of 200 voters, 140 said that they were in favor of this proposal. Compute the test statistic.

• A. z = 6.17

• B. z = 5.66

• C. z = 19.80

• D. None of the above

Multiple Choice

Tina wants to know if the proportion of people who buy burgers is at all affected by her open mic reading. If p=0.8 before her reading, what is an appropriate set of hypotheses?

• A.

  Ho: p = 0.8

  Ha: p > 0.8

• B.

  Ho: p = 0.8

  Ha: p < 0.8

• C.

  Ho: p ≠ 0.8

  Ha: p = 0.8

• D.

  Ho: p= 0.8

  Ha: p ≠ 0.8

Multiple Choice

When leaving for school, you make a judgement on these hypotheses. Ho: The weather will remain dry. Ha: It will rain. What are the results of the Type I and Type II errors?

• A.

  Type I: Needlessly carry around an umbrella all day. Type II: Get drenched

• B.

  Type I: Get drenched. Type II: Needlessly carry around an umbrella all day

• C.

  Type I: Carry umbrella & it rains. Type II: Carry no umbrella & it doesn't rain

• D.

  Type I: Get drenched. Type II: Carry umbrella & it rains

Multiple Choice

Two confidence interval estimates from the same sample are (0.72, 0.83) and (0.75, 0.81). One is at 95%, the other is at 99%. Which is which?

• A. (0.72, 0.83) is at 99%

• B. (0.72, 0.83) is at 95%

• C. Need to know sample size to determine this

• D. Need to know standard error to determine this

Unit Two: Regression and Probability

Modules 4-6

Main Ideas

• Calculate LSRL and use it to calculate predictions, interpret slope and y-intercept

• Calculate/interpret r and r²

• Identify/find probabilities of discrete and continuous random variables

• Standard Normal Curve

Multiple Choice

Find the area under the standard normal curve that lies to the left of z=2.1.

• A. 1.79%

• B. -1.79%

• C. 98.21%

• D. 0.98%

Multiple Choice

The scoring of modern IQ is such that Intelligence Quotients (IQs) have a normal distribution of μ= 100 and 𝞂 = 15.

Mensa International is a non-profit organization that accepts only people with IQ score within the top 2%. What level of IQ qualifies one to be a member of Mensa?

• 115
• 130.75
• 145
• 120

Multiple Choice

The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds.  What is the z-score for a player who runs a time of 5.6 seconds?

• -1.33
• 1.33
• 0.88
• 1.02

Multiple Choice

Given a continuous data with X~N(30,25). Find P(27<X<32).

• 0.3446

• 0.2743

• 0.3811

• 0.0703

Multiple Choice

Is r = -0.87 strong, moderate, or weak?

• strong

• moderate

• weak

Multiple Choice

Describe the correlation in the graph shown.

• Strong Negative
• Strong Positive
• Weak Negative
• Weak Positive

Multiple Choice

In linear regression, the residual refers to the difference between the predicted Y and actual Y values.

• True

• False

Multiple Choice

Linear regression analysis produces an equation of Y = 7 - 3.2X. This indicates that:

• An X value of 0 would would increase Y by 7.

• A 1 unit decrease in X results in a 3.2 unit decrease in Y.

• A 1 unit increase in X results in a 3.2 unit increase in Y.

• A 1 unit increase in X results in a 3.2 unit decrease in Y.

Multiple Choice

If x is temperature and y is coffee sales, use the following formula to determine the coffee sales on a 34° day.

y = -60x+6443

• $4403

• $4673

• $8483

• $6443

Multiple Choice

A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.

• y = 1.5x + 12

• y = 12x + 1.5

• y = 0.67x - 8

• y = -8x + 0.67

Multiple Choice

Which one of the following is discrete data?

• Sam is 160 cm tall
• Sam weighs 60 kg
• Sam ran 100 meters in 10.2 seconds
• Sam has two brothers and one sister

Multiple Choice

A survey found that 39% of the population owned dogs, 22% owned cats, and 8% of the population owned both a cat and a dog? Find the probability that a person owns a cat or a dog.

• 0.08

• 0.53

• 0.61

• 0.36

Multiple Choice

P(Pizza|Senior):

• 1/2

• 4/5

• 2/3

• 1/5

Multiple Choice

What is the probability that the person picked will be a boy given they speak German?

• 8/11

• 2/5

• 4/25

• 3/11

Multiple Choice

When would you expect the experimental probability of an event to get closer to equaling the theoretical probability of the event?

• When there are exactly 50 trials in the experiment.

• The fewer the number of trials in the experiment.

• The larger the number of trials in the experiment.

• This can't be determined.

Multiple Choice

40% of students in a school wore blue on a Spirit Day. If two students are randomly selected, what is the probability that both students will not be wearing blue?

• 0.16

• 0.36

• 0.24

• 0.60

Unit One: Descriptive Statistics and Graphs

Modules 1-3

Main Ideas

• Experiment vs Observational Study

• Two Way Tables

• SOCS (Shape Outlier Center Spread)

• Identify categorical/numerical variables

• Graphs of categorical/numerical variables

• Descriptive Statistics

Multiple Choice

The city of Smyrna wants to know which brand of paint will last longer. They paint 2 streets with brand A and two streets with brand B and checked which lasted longer. Is this a survey, observational study or an experiment?

• Survey

• Observational Study

• Experiment

Multiple Choice

At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. Using th Empirical Rule, what percentage of students at the high school have a GPA between 2.3 and 3.5?

• 68%

• 99.7%

• 95%

• 84%

Multiple Choice

In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval?

• 1084 to 1216 pounds

• 1106 to 1150 pounds

• 1106 to 1194 pounds

• 1128 to 1172 pounds

Multiple Choice

The data in the picture:

• is left skewed

• is right skewed

• symmetrical

Multiple Choice

The mean annual automobile insurance premium is RM950, with a standard deviation of RM175. Find the z-score that corresponds to a premium of RM1250.

• A. 1.13

• B. -1.13

• C. 1.71

• D. -1.71

Multiple Choice

The heights (in inches) of a sample of basketball players are shown:

76 79 81 78 82 78

Find the standard deviation.

• A. 2.2

• B. 6

• C. 2

• D. 4.8

Multiple Choice

Estimate the frequency of the class with the greatest frequency.

• A. 28

• B. 21

• C. 58

• D. 53

Multiple Choice

How many students got a perfect score on the test?

• 0
• 2
• 6
• 1

Multiple Choice

Identify the outlier for the given data?
23, 34, 27, 7, 30, 26, 28, 31, 34

• 7
• 23
• 31
• 34

Multiple Choice

What percent of students have a height between 58 inches and 60 inches?

• 25%

• 50%

• 75%

• 100%

Multiple Choice

• A
• B
• C
• D