Statistics Final
When four basketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select the order in which they shoot. What is the probability that they shoot free throws in alphabetical order? Assume each player has a different name.
=1/4! -> 4! = 24 so the answer is 1/24
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Resturant Order Accurate A- 315 B- 273 C- 248 D- 147 Order Not Accurate A- 34 B- 59 C- 37 D- 14 What is the probability of getting an order that is not accurate?
Add up all numbers in table. 1127. Add up all numbers for orders not accurate. 144 Take 144/1127=0.12777
Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in Celsius degrees.) Between 1.00 and 2.25
Find the graph where it is shaded in between the two values Probability: 0.1464 (spreadsheet 5.1)
The frequency distribution below represents frequencies of actual low temperatures recorded during the course of a 31-day month. Use the frequency distribution to construct a histogram. Do the data appear to have a distribution that is approximately normal? Class A 39-44 B 45-50 C 51-56 D 57-62 E 63-68 F 69-74 G 75-80 Frequency 1 2 7 7 8 3
Histogram: NO GAPS BETWEEN THE BARS Yes, it is approximately normal
Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Age (yr) when award was won 20-21 22-23 24-25 26-27 28-29 30-31 32-33 Frequency 31 36 14 3 5 2 2
Lower class limits: 20, 22, 24, 26, 28, 30, 32 Upper class limits: 21, 23, 25, 27, 29, 31, 33 Class width: (33-20)/7 = 1.857 (Always round to nearest number) 7 is the # of classes Class width = 2 Class midpoints: 20.5, 22.5, 24.5, 26.5, 28.5, 30.5, 32.5 Class boundaries: 19.5, 21.5, 23.5, 25.5, 27.5, 29.5, 31.5, 33.5 # of individuals in survey: add up frequencies = 93
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are foot lengths in inches of randomly selected women in a study of a country's military in 1988. Are the statistics representative of the current population of all women in that country's military? 9.5 9.1 8.7 9.1 9.6 8.9 8.5 9.8 10.1 8.7 8.7
Mean: 9.15 Median: 9.1 Mode: 8.7 Midrange: (max+min)/2 = (10.1 + 8.5)/2 = 9.3 Are the statistics representative of the current population of all women in that country's military? Since the measurements were made in 1988, they are not necessarily representative of the current population of all women in the country's military.
If we find that there is a linear correlation between the concentration of carbon dioxide in our atmosphere and the global temperature, does that indicate that changes in the concentration of carbon dioxide cause changes in the global temperature?
No. The presence of a linear correlation between two variables does not imply that one of the variables is the cause of the other variable.
In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it found that P(D)=0.740, where D is directly in person. If someone is randomly selected, what does P(D) represent, and what is its value?
P(D) is the probability of randomly selecting someone who does not choose a directin-person encounter as the most fun way to flirt 1-0.740 = 0.26
Identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster. A large company wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 60 customers and asks them about their level of satisfaction with the company.
Random
State whether the data described below are discrete or continuous, and explain why. The number of murders in different cities in a certain year
The data are discrete because the data can only take on specific values
What is different about the normality requirement for a confidence interval estimate of σ and the normality requirement for a confidence interval estimate of μ?
The normality requirement for a confidence interval estimate of σ is _stricter_ than the normality requirement for a confidence interval estimate of μ. Departures from normality have a _greater_ effect on confidence interval estimates of σ than on confidence interval estimates of μ. That is, a confidence interval estimate of σ is _less_ robust against a departure from normality than a confidence interval estimate of μ.
Which of the following is not a requirement for testing a claim about a population with σ not known?
The population mean, μ, is equal to 1.
Which of the following is NOT true about statistical graphs?
They utilize areas or volumes for data that are one-dimensional in nature.
The random variable x represents the number of phone calls an author receives in a day, and it has a Poisson distribution with a mean of 6.6 calls. What are the possible values of x? Is a value of x=2.2 possible? Is x a discrete random variable or a continuous random variable?
What are the possible values of x? = 0,1,2,3,... Is a value of x=2.2 possible? Is x a discrete random variable or a continuous random variable? A value of x=2.2 is not possible because x is a discrete random variable.
Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 71.6 Mbps. The complete list of 50 data speeds has a mean of x=15.21 Mbps and a standard deviation of s=17.43 Mbps. a. What is the difference between carrier's highest data speed and the mean of all 50 data speeds? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the carrier's highest data speed to a z score. d. If we consider data speeds that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the carrier's highest data speed significant?
a) To the find the difference, subtract highest measured speed to the mean 71.6 - 15.21= 56.39 b) To find the difference in standard deviation, take your answer from part and and divide it with the standard deviation 56.39 / 17.43= 3.24 c) Because the z score is the same as the value in part b, the z score is 3.24 d) Consider a value to be significantly low if its z score less than or equal to -2 or consider a value to be significantly high if its z score is greater than or equal to 2. Significantly high
Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below. TInterval (13.046,22.15) x=17.598 Sx=16.01712719 n=50 a) find the DF b) find critical value tα/2 corresponding to a 95% confidence interval c) Give a brief general description of the number of degrees of freedom
a) n-1= df 50-1= 49 b) 2.01 Click on view t-distribution, find degrees of freedom closest to yours, look under column "area in two tails" c) The number of degrees of freedom for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.
In the binomial probability formula, the variable x represents the ....
number of successes
Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
x = μ + (z x σ) x = 100 + (2.33 x 15) z-score in the chart (find number and find indicated z-score)
Claim: The mean pulse rate (in beats per minute) of adult males is equal to 69 bpm. For a random sample of 135 adult males, the mean pulse rate is 70.1 bpm and the standard deviation is 10.7 bpm. Complete parts (a) and (b) below
μ = 69 bpm Null (H0): μ = 69 bpm Alternative (H1): μ ≠ 69 bpm