1 Var. Quant. Data
This graph is not used for quantitative variables. (Pie chart, dotplot, stemplot, histogram)
What is a bar graph?
This is the formula for the chi square statistic.
What is χ2 = Σ (O-E)2/E?
An employee at a local pizza chain claims that their pizzas weigh 16 oz. To test this claim, you take a random sample of 25 pizzas. The sample mean weight is 12.4 oz, and the standard deviation is 2.5 ounces. This is the test that should be used.
What is a one-sample t-test?
This distribution calculates the probability of the first success.
What is a geometric distribution?
If a statistic has a sampling distribution whose mean is different from the true value of the parameter the statistic is estimating, then the statistic is this.
What is biased?
Data are collected on 25 truck drivers. This is not a variable for the data set. Select from truck color, driver age, driver address, truck license plate, and the number of trucks in the data set.
What is the number of trucks in the data set?
A survey was conducted in which male and female students were asked their favorite day to study. Possible responses were “Monday,” “Tuesday,” “Wednesday,” “Thursday,” “Friday,” “Saturday,” and “Sunday.” A chi-square test is used to determine whether the response to this question is independent of student gender. This is the number of degrees of freedom for the chi-square test.
What is df = 6?
df = (7 - 1) * (2 - 1) = 6
Devanshi wants to know if the mean age of high school teachers in New Jersey is less than 56 years. She obtains a random sample of 25 high school teachers, and finds a mean age of 54.4 years and a standard deviation of 9.2 years. This is her p-value.
What is 0.1966?
In TI-nspire: tTest(𝜇0=56, x̄=54.4, s=9.2, n=25, 𝜇<𝜇0)
Dorisa decides to roll a die 20 times. She recorded the number of times she rolled a 4 or more (a 4, 5, or 6). This distribution would be most appropriate to calculate the probability that Dorisa rolls a 4 or more (a 4, 5, or 6), 12 times.
What is a binomial distribution?
A larger sample size will (…) variability in a sampling distribution
What is minimize? (accept similar answers)
These are four things to look for when describing a quantitative variable.
What are shape, unusual features (outliers, gaps, or multiple clusters), center, and spread?
A bookstore claims it sells the following distribution of genres.
A manager uses a chi-square goodness-of-fit test to see whether the proportions in the samples he tests match what the bookstore claims. This is the null and alternative hypothesis for the test.
What is H0: pF = 0.20, pHF = 0.15, pR = 0.22, pSF = 0.38, pM = 0.05, and Ha: At least one of the proportions is different?
(The null hypothesis should represent the distribution of genres, and the alternative hypothesis should show that the distribution isn’t followed.)
Maria believes the number of dad jokes dads tell each day is significantly different than 95. She obtains a sample of 250 dads, who make a mean number of 145 dad jokes per day with a standard deviation of 16.4 dad jokes. She then calculates a p-value of 0.0647. This is the interpretation of the p-value.
What is: assuming that the number of dad jokes dads tell per day is 95, there is a probability of 0.0647 of obtaining a sample mean of 145 dad jokes per day or more extreme by random chance (accept similar answers)
These are the four requirements for a binomial distribution.
What are fixed number of trials, two possible outcomes, independent trials, and constant probability of success?
What is x̄ a point estimator for?
What is population mean (or mu (𝜇))?
Ten students were asked how much time (in hours) they spent studying for a specific test. These are the results:
| 2 | 1 | 1 | 3 | 4 | 2 | 7 | 5 | 3 | 2 |
This is the interquartile range of the number of hours spent studying in the list.
What is 2?
The median of Q1 (1, 1, 2, 2, 2) is 2. The median of Q3 (3, 3, 4, 5, 7) is 4. The IQR = Q3 - Q1. 4 - 2 = 2.
A random sample of 9th, 10th, 11th, and 12th grade students was taken in a magnet school. Students in the sample reported the number of hours of sleep they got the night before. The amount of sleep fell into three categories: less than 5 hours, 5-7 hours, and more than 7 hours. The data is shown below.
A manager uses a chi-square goodness-of-fit test to see whether the proportions in the samples he tests match what the bookstore claims. This is the null and alternative hypothesis for the test.
What is H0: pF = 0.20, pHF = 0.15, pR = 0.22, pSF = 0.38, pM = 0.05, and Ha: At least one of the proportions is different?
(The null hypothesis should represent the distribution of genres, and the alternative hypothesis should show that the distribution isn’t followed.)
Sophia wants to know if playing Resident Evil improves the reaction times of teens. She takes a random sample of 30 teens and records their reaction times before and after playing Resident Evil for 6 hours a day for a week. The data is displayed in the table below. Assume assumptions and conditions are met. At a significance level of 0.05, this is the confidence interval and its interpretation.
What is: we are 95% confident that the true mean difference between teen reaction times before and after playing Resident Evil for 6 hours a day for a week is between -0.720 seconds and -0.270 seconds.
In TI-npsire: tInterval(list of differences, frequency=1, confidence level=0.95)
This is the probability of rolling a die and getting a 3, 5, or 6 for the first time on your 9th, 10th, or 12th try.
What is 0.003662?
In TI-nspire: geomCdf(probability of success = 3/6, lower bound = 9, upper bound = 12)
n increases from 50 to 200, how does the standard deviation change?
What is decreases by a factor of 2? (accept similar answers)
The distribution of 19 shoe prices has a mean of $60 and a standard deviation of $4. Suppose an additional 20th shoe is added for sale at a price of $300. This is how and why the median of the shoe price distribution will change.
What is the median is not likely to change because it is resistant to outliers?
These are the conditions for a chi-square goodness-of-fit test.
What is data are counts, data must be from a random sample, n must be less than 10% of the population, and all expected counts must be greater than or equal to 5?
Yanna wants to see if, in 10 days of playing the game, new Brawl Stars players receive more Brawlers than veteran players. In the table below, she recorded the number of Brawlers each veteran account and each new account received. Assuming all assumptions and conditions are met, at a significance level of 0.05, this is Yanna’s conclusion.
What is: p-value = 0.00358 < 0.05. Reject the null hypothesis, the data do support that new Brawl Stars players receive more Brawlers than veteran players.
In TI-nspire: tTest_2Samp(list of veterans, list of new, frequency of veterans list=1, frequency of new list=1, Ha: 𝜇 veterans < 𝜇 new, not pooled)
This is the formula to find the probability of rolling a die 20 times and getting a 5 or 6, seven times. It is using nCk instead of a calculator function.
What is C(20, 7)*(⅓^7)*(⅔^13) or 0.182129
Maria wants to estimate the mean income of all households in Marlboro, NJ. She decides to randomly sample 1,000 households. She calculated the sample mean income to be $250,000. Is the sample mean income an unbiased or biased estimator of the population mean income?
What is an unbiased estimator?