Two Proportions
In a vote on the Clean water Bill, 49% of 205 Democrats voted for the bill. How many Democrats voted for this bill?
x = 101
What symbols represent the sample mean and the population mean?
sample mean = x̄
population mean = μ
What calculator functions might we use to test a claim about two dependent means (matched pairs) ?
T-Test / T-interval
What do the symbols r and ρ represent and what do they measure?
r = sample correlation coefficient
ρ = (rho) population correlation coefficient
They measure the strength of linear correlation.
What is the regression line?
The "line of best fit" which best fits the scatter plot of paired sample data.
Identify the original claim, null, and alternative hypothesis:
A study investigated rates of fatalities among patients with serious injuries. Among 61,909 patients transported by helicopter, 7,813 died. Among 61,566 patients transported by ground services, 5,775 died. Researchers want to test that the rate of fatalities is higher for patients transported by helicopter.
Original claim: p₁ > p₂
Null: p₁ = p₂
Alternative: p₁ > p₂
Determine whether the given sample is independent or dependent:
The effectiveness of a new headache medicine is tested by measuring the amount of time before a headache is cured for patients who are given the medicine and another group of patients who are given a placebo drug.
independent
TRUE or FALSE?
With ten matched pairs of heights, n = 20
FALSE
n = 10
What are some properties of the correlation coefficient?
1) -1 ≤ r ≤ 1
2) r does not change when either variable is converted to a different scale
3) r is not meant for nonlinear relationships
4) r is extremely sensitive to outliers
When do you use the regression equation to find the best predicted value of a given variable?
When there is evidence to support a linear correlation.
In a trial designed to test the effectiveness of aspirin in preventing heart disease, 11,037 male physicians were treated with aspirin and 11,034 male physicians were given placebos. Among the subjects treated in the aspirin group, 139 experienced heart attacks. Among the subjects given placebos, 547 experienced heart attacks. Use a 0.05 significance level to test the claim that aspirin has no effect on heart attacks.
There is sufficient evidence to reject the claim that aspirin has no effect on heart attacks.
Determine whether the given sample is independent or dependent:
As part of the National Health and Nutrition Examination survey, the Department of Health and Nutrition Services compared self reported heights (in) and measured heights (in) for teens between 12-16 years old.
Dependent
As part of a survey, the Department of Health and Human Services obtained self-reported heights (cm) and measured heights for teens aged 12-16. Run a hypothesis test and use a 0.01 significance level to test the claim that there is a difference between reported and measured heights.
Reported: 68 71 63 70 71 65 64
Measured:67.9 70.6 63.5 69.4 72.3 65.2 62.9
There is not sufficient evidence to support the claim that there is a difference between reported and measured heights.
TRUE or FALSE
The claim that there is a linear correlation between two variables can be written in symbolic form as:
ρ = 0
FALSE
Find the regression equation of the following sample data. (Round to three decimal places)
x: 10 7 13 16 9 18 15 15
y: 11 5 15 18 11 13 14 15
y = 2.394 + 0.804 x
In a study of drive through orders, it was found that 264 orders were accurate and 54 were not accurate at Burger King. At McDonalds, it was found that 329 order were accurate and 33 order were not accurate. Assume α = 0.05. Test the claim that Burger King and McDonalds have the same accuracy rates by constructing an appropriate confidence interval.
( -0.1295 , -0.0278 )
There is sufficient evidence to reject the claim that Burger King and Mcdonalds have the same accuracy rates.
Weights of quarters are carefully considered in the design of vending machines. Researchers measured pre-1964 and post-1964 quarters and came up with the following results. Use a 0.05 significance level and run a hypothesis test to test the claim that pre-1964 quarters have a mean weight that is greater than the mean weight of post-1964 quarters.
Pre-1964: n = 40 x̄ = 6.19267 g s = 0.087
Post-1964: n = 40 x̄ = 5.6393 g s = 0.06194
There is sufficient evidence to support the claim that pre-1964 quarters have a mean weight that is greater than the mean weight of post-1964 quarters.
A popular theory is that presidential candidates have an advantage if they are taller than their main opponent. Listed below are heights (cm) of presidents along with the heights of their main opponents. Use a 0.05 significance level to test the claim that for the population of heights of presidents and their main opponents, the differences have a mean greater than 0.
P: 185 178 175 183 193 173
O: 171 180 173 175 188 178
There is not sufficient evidence to support the claim that for the population of heights of presidents and their main opponents, the differences have a mean greater than 0.
Listed below are the number of registered boats in Florida and the number of manatee fatalities from encounters with boats for several recent years. Is there sufficient evidence to conclude that there is a linear correlation between number of registered boats and the number of manatee boat related fatalities? Assume α = 0.05
RB: 97 92 107 104 101 95 99
MD: 95 98 100 99 105 95 96
There is not sufficient evidence to support the claim that there is a linear correlation between number of registered boats and the number of manatee boat related fatalities.
Listed below are ages of best actress/actor each year at the Oscars. Find the best predicted value of the best actor’s age if the best actress’s age is 40. Assume α = 0.01
Actress Age: 28 30 36 42 45 37 31
Actor Age: 30 31 35 44 45 39 29
41 years old
In a random sample of males, it was found that 23 write with their left hand and 217 do not. In a random sample of females, it was found that 65 write with their left hand and 455 do not. Use a 0.01 significance level to test the claim that the rate of left handedness among males is less than that among females. Run a hypothesis test and construct an appropriate confidence interval.
There is not sufficient evidence to support the claim that the rate of left handedness is among males is less than that among females.
( -0.0848 , 0.02644 )
When visiting a city, a researcher records the ages of randomly selected passenger cars and randomly selected taxis. Use a 0.05 significance level to test the claim that the mean age of cars is greater than the mean age of taxis. (Run a hypothesis test)
Car 4 0 8 11 13 4 5 5 7 15 11
Taxi 8 9 3 6 6 0 8 7 4 10 5
There is not sufficient evidence to support the claim that the mean age of cars is greater than the mean age of taxis.
Who is your favorite statistics tutor?
BROOKE :)
Listed below are the bills for dinner and the amount of tips left at a local restaurant. Is there sufficient evidence to conclude that there is a linear correlation between the bill amounts and the tips left? Assume α = 0.01
Bill: 43.40 37.90 51.32 38.07 45.91
Tip: 7.00 5.00 11.00 7.93 9.00
There is not sufficient evidence to support the claim that there is a linear correlation between the bill amounts and the tips left.
Listed below are the overhead widths (cm) of seals and the weights (kg) of these same seals. Find the best predicted value of a seals height given that the seals overhead width is 8.6 cm. Assume α = 0.05
Overhead Width: 7.2 7.4 9.8 9.4 8.8 8.4
Weight: 116 154 245 202 200 191
188.7 kg