STATS FINAL STUDY
The probabilities of a customer purchasing 0, 1, 2, 3, or 4 games during a Steam sale are 0.2, 0.4, 0.25, 0.10, and 0.05 respectively. Calculate the expected value for the number of games a customer will purchase.
(0 x 0.2) + (1 x 0.4) + (2 x 0.25) + (3 x 0.10) + (4 x 0.05) 1.40
The average score on a communications exam was found to be 82 with a standard deviation of 5 points. Assuming the test scores were normally distributed, 15% of these scores were below what value?
76.8
A researcher from a health magazine gathered data to see whether there is a correlation between the number of hours training and the finishing time (in minutes) in a swim race. The following regression equation between the number of hours training and the finishing time was obtained: Finishing Time = 60.585 - 0.958 (Hours Trained). A person trained for 20 hours and finished the swim race in 45 minutes. What would be the residual for this person?
=60.585-0.958*20 =41.425 Now, the residual of a person is given by = 45 - 41.425 = 3.575
A Consumer Digests journalists asks the first 30 people leaving an Apple store if they believe laptops are too expensive. This example is _____________ sampling.
Convenience
Which of the following statements about a binomial random variable is TRUE?
Each of the observations or trials are independent.
The least-squares regression model between functional ability (x) and length of hospital stay (y) is given below: \hat{y} = 10.1 - 0.98xy^=10.1−0.98x
For every score increase in the functional ability, the length of hospital stay will decrease by 0.98 days. r2 = 0.98 take the square root of 0.98 answer: plus/minus 0.9083 -0.9083
The average completion time are measured for Death Stranding and Forza Horizon Five. Death Stranding has an average completion time of 110 hours with a standard deviation of 10 hours. Forza Horizon Five has an average completion time of 70 hours with a standard deviation of 5 hours. A certain player fully completed Death Stranding in 90 hours and completed Forza Horizon Five in 55 hours. Assuming the completion times are normally distributed, on which game did the person finish faster relative to the average?
Forza Horizon 5, because its z-score is farther below zero.
Which of the following is TRUE when standardizing using Z-scores? I. The shape of the distribution changes. II. The mean becomes 0. III. The standard deviation becomes 1.
II and III
A study found that the average household income for all United State citizens was $52,000. The value $52,000 is a:
PARAMETER
Histogram pic: It was determined that the outlier on the left resulted from a weight being incorrectly entered. This incorrect data point was removed from the data and a new histogram was made and all new statistics were calculated. Which of the following statements is true? When the incorrect data point is removed:
The mean will be larger, but the standard deviation will be smaller
If we calculate a 99% confidence interval (CI) instead of a 95% CI, then:
The midpoint of the CI would be unchanged, but the width would increase.
In testing the following hypotheses H0 : p = 0.58 vs Ha : p < 0.58, the p-value is found to be .0712, with a sample proportion of 0.48. Which of the following statements is true about the p-value?
The probability of observing a sample proportion smaller than 0.48 if the true proportion is actually 0.58 is .0712.
The boxplots below summarize the distributions of SAT verbal and math scores among students at an upstate New York high school:
The verbal scores are roughly symmetric while the math scores are skewed to the right.
A hypothesis test was conducted to test whether less than 50% of recent college graduates had a job offer prior to graduation. Assuming the null hypothesis is that only 50% have a job offer, a test statistic of z = -2.30 was found. When testing at the 5% significance level, which is the most appropriate conclusion?
There is sufficient evidence to conclude less than 50% of recent college graduates had a job offer prior to graduation.
A survey was conducted to determine the proportion of dog owners who vaccinate their pets on a yearly basis. Based on the response of 180 dog owners, an 80% confidence interval was calculated to be (0.52, 0.65). Which of the following statements is correct?
We are 80% confident that the population proportion of dog owners who vaccinate their pets is between 0.52 and 0.65.
The percentage of variability between function ability and length of hospital stay was found to be R-squared = 82.5%. Calculate the correlation coefficient.
r2 = 0.825 take the square root of 0.825 answer: plus/minus 0.9083 -0.9083
Which of the following type(s) of graphical display would be appropriate for analyzing the relationship between income and years of experience?
scatterplot
In a random sample of 850 consumers, 385 reported that they bought a PlayStation 5 above MSRP. Which of the following is a 95% confidence interval for the population proportion of consumers that bought a PlayStation 5 above MSRP?
(0.4194, 0.4864)
A national study found that 35% of households have access to fiber internet. In a random sample of 500 households, what is the probability that more than 40% of these households will have access to fiber internet?
0.0096
A 95% confidence interval for the proportion of U.S. adults who say that the activities of humans are contributing to an increase in global temperatures is (0.525, 0.579). The margin of error for this confidence interval is:
0.027 (0.579 - 0.525 /2)
The time it takes to complete Tunic follows a bell-shaped distribution with an average completion time of 14 hours with a standard deviation of 2.5. What is the probability a person completes Tunic in less than 10 hours?
0.0528
A survey was conducted in order to find out how many people like to watch comedy and horror movies. The results are given in the following contingency table. What is the probability a randomly selected person dislikes comedy and dislikes horror? Given that a randomly selected adult dislikes comedy movies, what is the probability they dislike horror movies?
0.10 15/120 = 0.15 0.10/0.15 = 0.6667
Zoe has a candy bowl that contains 15 pieces of M&Ms in which 9 are blue and 6 are green. Two M&Ms are to be selected with replacement. What is the probability both M&Ms selected are green?
0.16
In testing the hypotheses H_0: p = 0.46 \text{ vs } H_a: p \neq 0.46H0:p=0.46 vs Ha:p=0.46? The test statistic is calculated to be 1.35. Which of the following would be the correct p-value?
0.1770
Suppose it is known that 35% of households own a Nintendo Switch. If 10 people are selected at random, what is the probability that exactly 4 households in the sample own a Nintendo Switch?
0.2377
If P(A) = 0.4 and P(B) = 0.2, what is P(A or B) if A and B are independent events?
0.4 + 0.2 = 0.6 0.6 - (0.4)(0.2) = 0.52
A survey sent to homes across the United States asked how many cars a household has. The following probability distribution was collected from the results collected. Let X = number of cars owned. What is the probability that a household owns at least 2 cars?
0.55
It is known that 12% of kids are farsighted. A random sample of 170 kids is selected. What is the probability that at most 14% of this sample will be farsighted?
0.7881
A study found that in community colleges that 35% of students are choosing to continue to take online-only courses. Suppose we pick 8 community college students at random (thus, we can assume independence). What is that probability that at least 1 one of these students is taking an online-only course?
0.9861 1-(0.65^8)
In order to determine the effects of music and time of day on stress levels, 100 randomly selected subjects are assigned to one of four music groups: punk, metal, classical, or rap, and one of three time levels: morning, afternoon, or evening. The subjects' stress level is measured at the beginning of the study and after 5 months. How many treatments are there in this experiment?
4 music groups x 3 time levels = 12
A professor wishes to estimate the proportion of college students that have never cheated during an exam. She wishes to estimate the proportion to be within 4.15% with 96% confidence. How many college students are needed for the sample?
613 (2.054 / 0.0415)^2 x (0.5 x 1 - 0.5)
You collect data and test the hypotheses, H0 : p = 0.50 vs Ha : p does not equal 0.50. A P-value of 0.02 is obtained. Which of the following is true (hint: find \alphaα for each)?
A) A 99% confidence interval for p will not include the value 0.50. B) A 95% confidence interval for p will not include the value 0.50. C) A 90% confidence interval for p will not include the value 0.50. D.) B and C.
A humane society claims that 30% of U.S. households own a cat. In a random sample of 210 U.S. households, 35% say they own a cat. Is there enough evidence to show this percent has decreased? Identify the appropriate null and alternative hypotheses.
H0 : p = 0.30 vs Ha : p < 0.30
Which of the following will increase the width of a confidence interval for the proportion? I. Increasing the confidence levelII. Increasing the sample sizeIII. Decreasing the confidence levelIV. Decreasing the sample size
I and IV
In a regression analysis, which of the following statements are true? I. A residual plot with a pattern indicates that the regression model has good predictive power. II. A data point is influential if omitting it from the analysis gives a very different regression model. III. A data point that has leverage is not necessarily influential.
II and III
A research company decides to test the effect of a drug meant to reduce the intensity of migraine headaches. Two groups are tested. One group is given the drug and the other group is given a placebo. Length of relief from the headache is recorded. The test is done as a double-blind study. What is meant by double-blind?
Neither the patient nor the doctor administering the pill knows whether the pill is the actual drug or the placebo.
A study found that 1 out of 200 people own a gaming PC. If a random sample of 400 people is obtained, is the sampling distribution of the sample proportion of people that own a gaming PC approximately normal?
No, because np < 10.
The five-number summary for the salary of a sample of accountants is:
No, it is within 1.5(IQR) of the third quartile. 89,000-63500 = 25500 89000+1.5(25500)= 127,250
A box contains 14 Blu-ray movies, of which nine are action movies. Two Blu-rays are drawn at random from the box, without replacement. What is the probability that only one action movie is selected?
Now, from 14 phones, 2 phones can be drawn without replacement in 14*13 ways; because the first can be drawn in 14 ways and the second in 13 ways. 14 x 13 = 182 So, this choice can be made in 2 ways; the iphone can be selected in 9 ways; and the non iphone in 5 ways. 2 x 9 x 5 = 90 90/182
five number summary calculator ti-84
STAT, ENTER L1 STAT, CALC, 1-VAR STATS
In order to normally approximate the probability of a sample proportion, which of the following needs to be true:
Sample size must be less than 10% of the population size
A scientist claims that 69% of U.S. adults believe humans contribute to an increase in global temperature. A 95% confidence interval for the proportion of U.S. adults who say that the activities of humans are contributing to an increase in global temperatures is found to be (0.626, 0.674). Does this confidence interval support the scientist's claim?
Since 0.69 does not fall in the confidence interval, the scientist's claim is incorrect.
Suppose that a researcher in California wants to take a statewide survey regarding the legalization of all recreational drugs. The researcher creates a sample by randomly selecting 50 people from each county in the state. Which of the following terms best describes the type of sample that is being created?
Stratified
If two events are disjoint, then that must mean they are also dependent.
TRUE
When we sample with replacement, we have independent trials.
TRUE
A company wants to test a claim concerning the sensitivity of their vaccination. They are testing the null hypothesis that the sensitivity is 75% against the alternative that the sensitivity is less than 75%. The p-value for the hypothesis test was determined to be 0.032. Which of the following is a correct interpretation of this p-value?
The null hypothesis would be rejected at a 0.05 level but not at a 0.01 level.
Which situation best describes when to declare results statistically significant?
The p-value is less than the significance level and we reject the null hypothesis.
The following scatterplot shows an unusual point labeled X. How should this point be described?
The point X is influential
If the p-value exceeds the significance level, then that means we can reject the null hypothesis.
false
What percentage of those surveyed had a GED and are married? What percentage of those married had a college degree?
find intersecting number / TOTAL find intersecting number/ total within category
An experiment is being performed to test the effects of a new drug on reducing the level of someone's depression. 500 subjects diagnosed with depression participated in the experiment. The subjects' level of depression was measured prior to the experiment. After three months, their level of depression was measured again after using the drug. What type of experimental design is being used for this experiment?
matched pair
Suppose 18% of book readers say that fantasy is their favorite genre. If a random sample of 70 book readers is taken, what are the mean and standard deviation of the number of book readers that prefer fantasy? mu = 12.6 sigma = 3.2143
mu = n x p mu = 70 x 0.18 = 12.6 sigma = sqrt* (np(1-p)) sqrt*(70x0.18x(1-0.18)) = 3.2143
In order to determine the proportion of students who favor an increase in fees to support a new gym, questionnaires were emailed to all students at the college. 10% of the students returned the questionnaires. The most significant bias introduced here is:
non-response bias
A survey among freshmen at SDSU showed that the number of hours spent studying for final exams was normally distributed with an average of 20 hours and a standard deviation of 9 hours. What is the probability a randomly selected freshman studies between 35 and 43 hours for final exams?
p (35-20/9 < x-mu/sigma , 43-20/9) p(15/9 < z < 23/9) p(1.67 < z < 2.56 cumulative z score : 0.9948 and 0.9525 0.9948-0.9525 = 0.0423
A survey found that 80% of individuals in the US have some type of streaming service. A random sample of 10 individuals is selected. What is the probability that at least 7 of these individuals have some some type of streaming service?
p = 0.80 n = 10 1-BINOMCDF(10, 0.80, 6) = 0.1209 1- 0.1209 = 0.8791
A recent article has found that 15% of adults have renters insurance. Suppose we randomly select 120 adults and find that 18% of them have renters insurance. Which of the following correctly describes the distribution for the sample proportion of adults in our sample who have renters insurance?
p ~ AN (0.15, 0.0326)
Pre-study scores versus post-study scores for a class of 120 college freshman English students were considered. The residual plot for the least-squares regression line showed no pattern. The least-squares regression line was {y} = 0.2 + 0.9xy=0.2+0.9x with a correlation coefficient r = 0.85r=0.85. What percent of the variation of the post-study scores can be explained by the variation in pre-study scores?
r^2 x 100 (0.85)^2 x 100 = .7225 or 72.3%
Which of the following variables is continuous?
time spent listening to music
