STATS FINAL
a) P(exactly 5) = 0.209 b) P(at least six) = 0.183 c) P(less than four) = 0.358 (explanation) Sample size, n = 10 Proportion of adults that have very little confidence in newspapers, p = 41% p = 0.41 q = 1 - 0.41 = 0.59 This is a binomial distribution question. look up whatever the hell that is
41% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.
Ho=μ≤860 Ha: μ>860 (claim) The critical value is 1.64 The rejection region is z>1.64. Standardized test statistic 1.88 Reject H0 because the standardized test statistic is in the rejection region. At the 5% significance level, there isis enough evidence to support the claim that the mean monthly residential electricity consumption in a certain region is greater than 860 kWh.
A company claims that the mean monthly residential electricity consumption in a certain region is more than 860 kiloWatt-hours (kWh). You want to test this claim. You find that a random sample of 64 residential customers has a mean monthly consumption of 890 kWh. Assume the population standard deviation is 128 kWh. At α=0.05, can you support the claim? Complete parts (a) through (e).
836 https://www.youtube.com/watch?v=1VrWgpCEmaY&feature=youtu.be
A local elemenatary school has 950 students. 88% of the students who were surveyed said they are in favor of having ipads offered to students for school and home use. Which of the following numbers of students best represents the likely number of students who would like to have ipads offered for school and home use?
A meal can be chosen in 240 ways.
A restaurant offers a $12 dinner special that has 6 choices for an appetizer, 10 choices for an entrée, and 4 choices for a dessert. How many different meals are available when you select an appetizer, an entrée, and a dessert?
a. Use the simplified Addition Rule to find the probability. The rule states that if A and B are mutually exclusiveevents, then P(A or B)=P(A)+P(B). This translates to the following equation. P(nine or ten)=P(nine)+P(ten) Recall that in a deck of cards there are four of each type of card (two, three, four, five, six, seven, eight, nine, ten, jack, queen, king, and ace). These cards are divided into four suits, with one in each suit (hearts, diamonds, clubs, and spades). What is the probability of drawing a nine? P(nine)=n(nine)/n(S)=1/13 P(ten)=n(ten)/n(s)=1/13 P(nine or ten)= 1/13+1/13=0.154 b. The simplified Addition Rule for can be extended to more than two mutually exclusive events. P(E or F or G...)=P(E)+P(F)+P(G)+... P(nine or ten or six)=P(nine)+P(ten)+P(six) P(six)=n(six)/n(S)=1/13 P(nine or ten or six)=0.231 c. Use the Addition Rule to find the probability. The general rule states that for any two events A and B, P(A or B)=P(A)+P(B)−P(A and B). P(seven or spade)=P(seven)+P(spade)−P(seven and spade) The probability of drawing a seven from a deck of cards is 1/13, and the probability of drawing a spade is 1/4. What is the probability of drawing a seven that is also a spade from a deck of cards? P(seven and spade)=1/52 P(seven or spade)=1/13+1/4-1/52 just hope for the best, basically
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a nine or ten. (b) Compute the probability of randomly selecting a nine or ten or six. (c) Compute the probability of randomly selecting a seven or spade.
use https://www.socscistatistics.com/tests/ztest/zscorecalculator.aspx its easy peasy
A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1457 and the standard deviation was 312. The test scores of four students selected at random are 1870, 1190, 2150, and 1330. Find the z-scores that correspond to each value and determine whether any of the values are unusual.
0.56 https://www.youtube.com/watch?v=E3IWhLkoWQ4&feature=youtu.be
A surgical treatment has a success rate of 0.75. Two patients will be having this surgery. Assuming the results are independent for the two patients, what is the probability that both of them will be successful?
The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 0.516
According to a study, 86% of K-12 schools or districts in a country use digital content such as ebooks, audio books, and digital textbooks. Of these 86%, 6 out of 10 use digital content as part of their curriculum. Find the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum.
z = -1.00 https://www.youtube.com/watch?v=5lwzGB9xeZQ
Corporate training can involve the use of standardized tests to determine how well their employees retain professional development training. Suppose the standardized test used has a normal distribution with a mean of 82 and a standard deviation of 3. If one employee had a score of 79, what is the employee's z-score?
Permutations
Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. The number of ways 16 people can line up in a row for concert tickets.
Combination? just a guess though
Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. The number of ways a four-member committee can be chosen from 15 people.
Discrete, because home attendance is a random variable that is countable.
Decide whether the graph represents a discrete random variable or a continuous random variable. The home attendance for football games at a university
The pie chart shows the percentages as parts of the whole. The Pareto chart shows the rankings of the seasons.
Describe the difference in how the pie chart and the Pareto chart show patterns in the data. Choose the correct answer below.
The range of values for the correlation coefficient is −1 to 1, inclusive
Describe the range of values for the correlation coefficient.
Determine if the survey question is biased. If the question is biased, suggest a better wording. Why is eating cake bad for you?
Determine if the survey question is biased. If the question is biased, suggest a better wording. Why is eating cake bad for you?
Event C has 22 outcome(s). Is the event a simple event?-No, because event C has more than one outcome
Determine the number of outcomes in the event. Decide whether the event is a simple event or not. You randomly select one card from a standard deck of 52 playing cards. Event C is selecting a red four.
The statement is true.
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. The mean is the measure of central tendency most likely to be affected by an outlier.
The random variable is discrete, because it has a countable number of possible outcomes.
Determine whether the random variable x is discrete or continuous. Explain. Let x represent the number of hits to a website in a day.
False. In a frequency distribution, the class width is the distance between the lower or upper limits of consecutive classes.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. In a frequency distribution, the class width is the distance between the lower and upper limits of a class.
In the z-test using rejection region(s), the test statistic is compared with critical values. The z-test using a P-value compares the P-value with the level of significance α.
Explain the difference between the z-test for μ using rejection region(s) and the z-test for μ using a P-value.
To find the area between two z-scores, find the area corresponding to each z-score in the standard normal table. Then subtract the smaller area from the larger area. Note that either technology or the standard normal table can be used to find these areas, but for the purposes of this explanation, the table will be used. What is the area that corresponds to you find the number it tells you in the z score column and you go to .00 z=−1 in the standard normal table?=0.1587 z=0.7 in the standard normal table?=0.7580 Now subtract the smaller area from the larger area to find the area of the indicated region under the standard normal curve. Area= 0.7580−0.1587=0.5993 Thus, the area between z=−1 and z=0.7 under the standard normal curve is 0.5993.
Find the area of the indicated region under the standard normal curve.
First, find the parameters of the sampling distribution using the Central Limit Theorem (the ux thing = 60,000) To find σ-x, use the fact that the standard deviation of the distribution of the sample mean is equal to the population standard deviation divided by the square root of the sample size. o-x=894.959 Now find the z-score for the value x=57,500. Recall that the standard normal z-score corresponding to x is given by the equation below. ok so then you 57,500-60,000/894.959 and you get -2.79 While either technology or a normal distribution table can be used to answer this question, for the purposes of this explanation, use technology. To find the probability that x is less than 57,500, find the area under the standard normal curve to the left of z=−2.79. Px<57,500 = P(z<−2.79) = 0.0026 Therefore, the probability that the mean salary of the sample is less than $57,500 is 0.0026. Use the probability to determine whether or not a sample mean of less than $57,500 is an unusual event. Recall that values lying more than two standard deviations from the mean are unusual, and values lying more than three standard deviations from the mean are very unusual. Use the facts that P(z<−2)≈0.0228 and P(z<−3)≈0.0013 when making a determination. you might just have to cut your losses here it makes no sense
Find the probability and interpret the results. If convenient, use technology to find the probability. The population mean annual salary for environmental compliance specialists is about $60,000. A random sample of 42 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $57,500? Assume σ=$5,800.
use https://www.socscistatistics.com/pvalues/normaldistribution.aspx and be careful with rounding
Find the P-value for a left-tailed hypothesis test with a test statistic of z=−1.70. Decide whether to reject H0 if the level of significance is α=0.05.
MIN: 1 Q1: 5.25 Q2: 7 Q3: 8.75 MAX: 9
Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 3 8 8 6 2 9 8 7 9 6 9 5 1 6 2 9 8 7 7 9
A sample is a subset of a population.
How is a sample related to a population?
The sample space is {21,23,25,27,29} There are 55 outcome(s) in the sample space.
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Randomly choosing an odd number between 20 and 30
SAMPLING: Cluster sampling is used, since the disaster area is divided into grids, and some of those grids are selected and everyone in those grids is interviewed. BIAS: Certain grids may have been much more severely damaged than others. The grids that are selected may not be representative in terms of damage AND Certain grids may have been much more severely damaged than others. Severely damaged grids may have fewer occupied households.
Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. After a tornado, a disaster area is divided into 150 equal grids. Twenty of the grids are selected, and every occupied household in the grid is interviewed to help focus relief efforts on what residents require the most.
SAMPLING: Stratified sampling is used, since the field is divided into subplots and a random sample is taken from each subplot. BIAS: Certain subplots may have more or fewer carrot plants than others. Samples from these subplots may bias the overall sample.
Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. Carrots are planted on a 54-acre field. The field is divided into one-acre subplots. A sample is taken from each subplot to estimate the harvest.
SAMPLING: Convenience sampling is used, because students are chosen due to convenience of location. BIAS: The sample only consists of members of the population that are easy to get. These members may not be representative of the population AND Because of the personal nature of the question, students may not answer honestly.
Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. Assume the population of interest is the student body at a university. Questioning students as they leave an athletic facility, a researcher asks 365 students about their dating habits.
10924.72 https://www.youtube.com/watch?v=n8tYT58AH7U
If the annual health care cost per person can be approximated by the least squares line y = 185.84x + 146 where x = 0 corresponds to the year 1960, find the approximate health care cost per person in 2018.
A. Reject H0, because t>1.859. B. Fail to reject because t<1.859 C. Fail to reject because t<1.859 D. Fail to reject H0 because t<1.859
State whether the standardized test statistic t indicates that you should reject the null hypothesis. Explain. (a) t=1.869 (b) t=0 (c) t=1.842 (d) t=-1.873
The equation of the regression line is y=0.67x+13.82 A. Predict the girth for a length of 140 cm=107.62 B. 172 cm=It is not meaningful to predict this value of y because x=172 is well outside the range of the original data C. 123.7 D. 119.68
The accompanying data are the length (in centimeters) and girths (in centimeters) of 12 harbor seals. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x=140 cm (b) x=172 cm (c) x=164 cm (d) x=158 cm
The equation of the regression line is y=−0.19x+6.46 (use https://www.socscistatistics.com/tests/regression/default.aspx) A. ERA FOR 5 WINS: not meaningful because x=5 is well outside the ragne B. ERA FOR 10 WINS: 4.56 C. ERA FOR 19 WINS: 2.85 D. ERA FOR 15 WINS: 3.61
The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x=5 wins (b) x=10 wins (c) x=19 wins (d) x=15 wins
a.The student is male or received a degree in the field The probability is 0.497 (might be wrong) b. The student is female or received a degree outside of the field. The probability is 0.909 c. The student is not female or received a degree outside of the field. The probability is 0.935
The accompanying table shows the numbers of male and female students in a certain region who received bachelor's degrees in a certain field in a recent year. A student is selected at random. Find the probability of each event listed in parts(a) through (c) below.
RANGE: 11 MEAN: 16.9 VARIANCE: 11.6 STANDARD DEVIATION: 3.4
The ages (in years) of a random sample of shoppers at a gaming store are shown. Determine the range, mean, variance, and standard deviation of the sample data set. 12, 21, 23, 15, 14, 16, 20, 17, 15, 16
0.159 https://www.youtube.com/watch?v=rNYI18eh7BQ
The amounts of time a student studies for a college-level math test are normally distributed, with a mean of 2.5 hours and a standard deviation of .5 hours. Use the normalcdf function in the calculator to find the probability that the time a randomly selected student studies for a college-level math test is less than 2 hours.
look at camera roll
The data represent the time, in minutes, spent reading a political blog in a day. Construct a frequency distribution using 5 classes. In the table, include themidpoints, relative frequencies, and cumulative frequencies. Which class has the greatest frequency and which has the least frequency?
Strong positive relationship
The graph below is the shoe sizes and heights (in inches) of 14 girls. Determine the strength of the relationship between shoe sizes and heights.
Nominal. The data are categorized using numbers, but no mathematical computations can be made.
The jersey numbers for players on a basketball team are listed below. Identify the level of measurement of the data set. Explain your reasoning.
MEDIAN: 4. IT REPRESENTS THE CENTER MODE: 3. The mode(s) does (do) not represent the center because it (one) is the smallest data value.
The number of credits being taken by a sample of 13 full-time college students are listed below. Find the mean, median, and mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why.4,4,7,7,4,3,3,3,5,3,3,3,6
It would be unusual because the probability of having no HD televisions is less than 0.05. We say a event is unusual if the probability of that event to get happen is less than 0.05. From the table it is given that, the probability of having no HD televisions is 0.030 which is less than 0.05.
The number of televisions (HD) per household in a small town Televisions 0 1 2 3 Households 78 406 718 1399 P(x) 0.030 0.156 0.276 0.538
RANGE: 13 POPULATION MEAN: 8.3 POPULATION VARIANCE: 19.2 POPULATION STANDARD DEVIATION: 4.4
The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set. 2, 10, 15, 5, 11, 6, 15, 10, 3, 6
you're just gonna have to check your camera roll for this one man
The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n=69, find the probability of a sample mean being less than 23.1 if μ=23 and σ=1.3.
MEDIAN: 44. IT REPRESENTS THE CENTER MODE: 44. IT REPRESENTS THE CENTER
The tuition and fees (in thousands of dollars) for the top 14 universities in a recent year are listed below. Find the mean, median, and mode of the data, if possible. If any of these measures cannot be found or a measure does not represent the center of the data, explain why. 42 42 42 44 46 35 47 44 39 47 47 44 44 44
Interval. The data can be ordered and differences between data entries are meaningful, but a zero entry is not an inherent zero
The years that a particular team won the world series are shown below. Determine the level of measurement of the data set. Explain your reasoning
The dependent variable increases.
Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases?
H0:μ=52,800 Ha:μ≠ 52,800 Standardized test statistic=1.47 The critical value(s) is(are) 2.101, −2.101. Fail to reject. There is not enough evidence to reject the claim.
Use a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed. Claim: μ=52,800; α=0.05 Sample statistics: x=53,674, s=2600,
Identify the null and alternative hypotheses. Choose the correct answer below. Ho=u≤1180 Ha=μ>1180 standardized test statistic: 2.05
Use technology to help you test the claim about the population mean, μ, at the given level of significance, α, using the given sample statistics. Assume the population is normally distributed. Claim: μ>1180; α=0.08; σ=207.74. Sample statistics: x=1204.56,
The party of registered voters in the county
Use the Venn diagram to identify the population and the sample, choose the correct description of the population
The party of registered voters in the county who voted in the last election
Use the Venn diagram to identify the population and the sample, choose the correct description of the sample
CORRECT DATA ENTRIES: 17,17,18,18,18,19,19,19,19,19,20,21,21,22,23 MAXIMUM DATA ENTRY: 23 MINIMUM DATA ENTRY: 17
Use the dot plot to list the actual data entries. What is the maximum data entry? What is the minimum data entry?
A. there are 7 classes B. the least frequency is about 20, the greatest frequency is about 290 C. the class width is 5 D. About half of the employees' salaries are between $40,000 and $49,000
Use the frequency histogram to complete the following parts. (a) Determine the number of classes. (b) Estimate the greatest and least frequencies. (c) Determine the class width. (d) Describe any patterns with the data.
least: 20, greatest: 270
Use the frequency histogram to estimate the least and greatest frequency.
The class width is 14. CORRECT LOWER CLASS LIMITS:10,24,38,52,66,80 CORRECT UPPER CLASS LIMITS: 23,37,51,65,79,93
Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. minimum=10, maximum=89, 6 classes
The class width is 15 CORRECT LOWER CLASS LIMITS: 17,32,47,62,77,92,107,122 CORRECT UPPER CLASS LIMITS: 31,46,61,76,91,106,121,136
Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. minimum=17, maximum=133, 8 classes
The class width is 15. Figure out the rest yourself its not hard
Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. minimum=18, maximum=133, 8 classes
Find the z-score that corresponds to an area of 0.9942 by locating 0.9942 in the standard normal table. The values at the beginning of the corresponding row and at the top of the corresponding column give the z-score. What is the value at the beginning of the row where the cumulative area 0.9942 can be found? = 2.5 Therefore, the z-score begins with 2.5. Now, find the value nearest 0.9942 in row 2.5. The column heading on the nearest value is the hundredths place of the z-score. If 0.9942 lies halfway between two entries, then the hundredths place is the smaller of the two column headings and there is a 5 in the thousandths place. What is the z-score for the cumulative area 0.9942? z=2.525 (used https://www.danielsoper.com/statcalc/calculator.aspx?id=19)
Use the standard normal table to find the z-score that corresponds to the cumulative area 0.9942. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores.
There appears to be a strong positive linear correlation. As the years of experience of the registered nursesincrease, salaries tend to increase
Using the scatter plot of the registered nurse salary data shown, what type of correlation, if any do you think the datahave? Explain.
Descriptive statistics and inferential statistics.
What are the two main branches of statistics?
In an experiment, a treatment is applied to part of a population and responses are observed. In an observational study, a researcher measures characteristics of interest of a part of a population but does not change existing conditions
What is the difference between an observational study and an experiment?
r=−0.871
Which value of r indicates a stronger correlation: r=0.756 or r=−0.871? Explain your reasoning.
It is usually impossible to count the entire population.
Why is a sample used more often than a population?
A. Rolling a die twice B. Drawing one card from a standard deck, not replacing it, and then selecting another card
(a) List an example of two events that are independent. (b) List an example of two events that are dependent.
0.2558 https://www.youtube.com/watch?v=JX31ltYPXL4
77% of Kroger shoppers say they use their Kroger card because of the discounts program. You randomly select 12 Kroger shoppers and ask each to name the reason he or she uses their Kroger card. Use the binomialpdf function in the calculator to find the probability that the number of shoppers who say they use their Kroger card because of the discounts program is exactly 10.
