13 Balls are in an urn. 4 are blue, 3 are black, 6 are red.
If two balls are taken out of the urn at the same time, what is the probability that the balls are of different color? What is the probability that the balls would be different colors if you took one ball and put it back before drawing the second?
In: Statistics and Probability
Use the given information to find the number of degrees of
freedom, the critical values
chi Subscript Upper L Superscript χ2L and chi Subscript Upper R
Superscript χ2R, and the confidence interval estimate of sigmaσ. It
is reasonable to assume that a simple random sample has been
selected from a population with a normal distribution. Nicotine in
menthol cigarettes 98% confidence; nequals=26sequals=0.22mg.
Area to the Right of the Critical Value
Degrees of Freedom 0.995 0.99
0.975 0.95 0.9 0.1
0.05 0.025 0.01
0.005 Degrees of Freedom
1 - - 0.001
0.004 0.016 2.706
3.841 5.024 6.635
7.879 1
2 0.01 0.02 0.051
0.103 0.211 4.605
5.991 7.378 9.21
10.597 2
3 0.072 0.115 0.216
0.352 0.584 6.251
7.815 9.348 11.345
12.838 3
4 0.207 0.297 0.484
0.711 1.064 7.779
9.488 11.143 13.277
14.86 4
5 0.412 0.554 0.831
1.145 1.61 9.236
11.071 12.833 15.086
16.75 5
6 0.676 0.872 1.237
1.635 2.204 10.645
12.592 14.449 16.812
18.548 6
7 0.989 1.239 1.69
2.167 2.833 12.017
14.067 16.013 18.475
20.278 7
8 1.344 1.646 2.18
2.733 3.49 13.362
15.507 17.535 20.09
21.955 8
9 1.735 2.088 2.7
3.325 4.168 14.684
16.919 19.023 21.666
23.589 9
10 2.156 2.558
3.247 3.94 4.865
15.987 18.307 20.483
23.209 25.188 10
11 2.603 3.053
3.816 4.575 5.578
17.275 19.675 21.92
24.725 26.757 11
12 3.074 3.571
4.404 5.226 6.304
18.549 21.026 23.337
26.217 28.299 12
13 3.565 4.107
5.009 5.892 7.042
19.812 22.362 24.736
27.688 29.819 13
14 4.075 4.66 5.629
6.571 7.79 21.064
23.685 26.119 29.141
31.319 14
15 4.601 5.229
6.262 7.261 8.547
22.307 24.996 27.488
30.578 32.801 15
16 5.142 5.812
6.908 7.962 9.312
23.542 26.296 28.845
32 34.267 16
17 5.697 6.408
7.564 8.672 10.085
24.769 27.587 30.191
33.409 35.718 17
18 6.265 7.015
8.231 9.39 10.865
25.989 28.869 31.526
34.805 37.156 18
19 6.844 7.633
8.907 10.117 11.651
27.204 30.144 32.852
36.191 38.582 19
20 7.434 8.26 9.591
10.851 12.443 28.412
31.41 34.17 37.566
39.997 20
21 8.034 8.897
10.283 11.591 13.24
29.615 32.671 35.479
38.932 41.401 21
22 8.643 9.542
10.982 12.338 14.042
30.813 33.924 36.781
40.289 42.796 22
23 9.26 10.196
11.689 13.091 14.848
32.007 35.172 38.076
41.638 44.181 23
24 9.886 10.856
12.401 13.848 15.659
33.196 36.415 39.364
42.98 45.559 24
25 10.52 11.524
13.12 14.611 16.473
34.382 37.652 40.646
44.314 46.928 25
26 11.16 12.198
13.844 15.379 17.292
35.563 38.885 41.923
45.642 48.29 26
27 11.808 12.879
14.573 16.151 18.114
36.741 40.113 43.194
46.963 49.645 27
28 12.461 13.565
15.308 16.928 18.939
37.916 41.337 44.461
48.278 50.993 28
29 13.121 14.257
16.047 17.708 19.768
39.087 42.557 45.722
49.588 52.336 29
30 13.787 14.954
16.791 18.493 20.599
40.256 43.773 46.979
50.892 53.672 30
40 20.707 22.164
24.433 26.509 29.051
51.805 55.758 59.342
63.691 66.766 40
50 27.991 29.707
32.357 34.764 37.689
63.167 67.505 71.42
76.154 79.49 50
60 35.534 37.485
40.482 43.188 46.459
74.397 79.082 83.298
88.379 91.952 60
70 43.275 45.442
48.758 51.739 55.329
85.527 90.531 95.023
100.425 104.215 70
80 51.172 53.54
57.153 60.391 64.278
96.578 101.879 106.629
112.329 116.321 80
90 59.196 61.754
65.647 69.126 73.291
107.565 113.145 118.136
124.116 128.299 90
100 67.328 70.065
74.222 77.929 82.358
118.498 124.342 129.561
135.807 140.169 100
0.995 0.99
0.975 0.95 0.9 0.1
0.05 0.025 0.01
0.005
Area to the Right of the Critical
Value
Degrees of Freedom
n-1 Confidence interval or hypothesis test for a
standard deviation sigma or variance sigma superscript
2
k-1 Goodness-of-fit with k categories
(r-1)(c-1) Contingency table with r rows and c
columns
k-1 Kruskal-Wallis test with k samples
In: Statistics and Probability
Prior to a set of compensation policy changes at a company 31% of the employees surveyed said that they liked their job very much, 50% said that they liked their job moderately, and the remaining employees said that they were dissatisfied with their job. Now, in a survey of 194 employees, 76 said they liked their job very much, 105 said that they liked their job moderately, and the remaining employees said that they were dissatisfied with their job. When testing (at the 10% level of significance) whether the proportions have changed, what is the critical value? (please round your answer to 3 decimal places)
In: Statistics and Probability
In: Statistics and Probability
The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of
223
milligrams per deciliter and a standard deviation of
37.2
milligrams per deciliter.(a) What percent of the men have a total cholesterol level less than
228
milligrams per deciliter of blood?(b) If
251
men in the 35-44 age group are randomly selected, about how many would you expect to have a total cholesterol level greater than 259
milligrams per deciliter of blood?(a) The percent of the men that have a total cholesterol level less than
228
milligrams per deciliter of blood is
nothing%.
(Round to two decimal places as needed.)
In: Statistics and Probability
1. Three fair dices were rolled.
(a) How many possible outcomes there will be, if the number in each
dice was recorded and the order of dices are considered.
(b) How many possible outcomes there will be, if the sum of the
dices are recorded.
(c) What is the probability of getting a result with the sum of the
three dices exactly equals to 6?
(d) What is the probability of getting a result with the sum of the
three dices less than 6?
2. Seven fair coins were flipped and
there outcomes of each coin (head or tail)
were recorded.
(a) How many possible outcomes there will be, if the order of coins
are considered?
(b) How many possible outcomes with exactly 3 heads(and 4
tails)?
(c) What is the probability of getting a result with exactly 3
heads (and 4 tails)?
(d) What is the probability of getting a result with less than 2
head(and more than 5 tails)?
In: Statistics and Probability
According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the type I and type II errors in this case, consequences of each error type for this situation, and the appropriate alpha level to use. According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the type I and type II errors in this case, consequences of each error type for this situation, and the appropriate alpha level to use.
In: Statistics and Probability
The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location.
Ceremonial Ranking | Cooking Jar Sherds | Decorated Jar Sherds (Noncooking) | Row Total |
A | 90 | 45 | 135 |
B | 93 | 52 | 145 |
C | 76 | 78 | 154 |
Column Total | 259 | 175 | 434 |
Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: Ceremonial ranking and pottery type are
independent.
H1: Ceremonial ranking and pottery type are not
independent.H0: Ceremonial ranking and pottery
type are not independent.
H1: Ceremonial ranking and pottery type are
independent. H0:
Ceremonial ranking and pottery type are not independent.
H1: Ceremonial ranking and pottery type are not
independent.H0: Ceremonial ranking and pottery
type are independent.
H1: Ceremonial ranking and pottery type are
independent.
(b) Find the value of the chi-square statistic for the sample.
(Round the expected frequencies to at least three decimal places.
Round the test statistic to three decimal places.)
Are all the expected frequencies greater than 5?
YesNo
What sampling distribution will you use?
chi-squareStudent's t binomialuniformnormal
What are the degrees of freedom?
(c) Find or estimate the P-value of the sample test
statistic. (Round your answer to three decimal places.)
p-value > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005
(d) Based on your answers in parts (a) to (c), will you reject or
fail to reject the null hypothesis of independence?
Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis. Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the
application.
At the 5% level of significance, there is sufficient evidence to conclude that ceremonial ranking and pottery type are not independent.At the 5% level of significance, there is insufficient evidence to conclude that ceremonial ranking and pottery type are not independent.
In: Statistics and Probability
EatWell Inc., a large fast-food chain company of Canada, wants to test two versions of a new product before launching its full production. They select a random sample of individuals among their regular clients and ask them to participate in an experiment to rate the product according to an assessment grid worth 20 points. The 15 individuals who accepted to participate had to come to a specific company location on two occasions during a given week to test the two versions of the product. It was a randomized experiment in which the version assigned to participants during their first visit was selected at random and participants did not know which version they were rating.
Individual Version A Version B
1 17 16
2 17 18
3 20 17
4 11 15
5 15 12
6 16 15
7 15 14
8 16 13
9 12 12
10 16 13
11 19 18
12 14 14
13 17 15
14 18 16
15 18 17
a) Comment on the distribution of the ratings for the two versions of the product and decide which statistical test is the most appropriate for this type of data. Justify your selection based on the assumptions and conditions required for the most appropriate test selected.
b) Regardless of your answer in a) above, perform a relevant parametric test using a 10% significance level to determine if there is a difference between the two versions of the product. Make sure you show your Minitab or other software output along with an interpretation of the results (manual calculations are not required here).
c) Now, perform a Wilcoxon signed rank test to verify if there is a significant difference at the 10% level between the two versions of the product based on these ratings. Show your manual calculations including the T+ and T- statistics and conclude based on the critical value approach.
d) Use Minitab or other software to perform the test in c) above and comment on the computed Pvalue and your conclusion in c). e) Compare your results from the parametric and non-parametric tests above and state what the final conclusion regarding the two versions of the product should be.
In: Statistics and Probability
What is the probability that the woman has a diastolic blood pressure between 60 and 90 mmHg?
1. Suppose you have a variable X~N(8, 1.5).
Among females in the US between 18 and 74 years of age, diastolic blood pressure is normally distributed with mean µ=77mmHg and standard deviation σ=11.6mmHg
Note- 0.87 was not correct
In: Statistics and Probability
QUESTION 1:
An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used yy (in cubic feet) to heat the home and outside temperature xx ( in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65 oFoF) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be:
yˆ=y^=85 + 14x
The predicted amount of gas used when the outside temperature is 15 degree-days
is about: cubic feet. (Answer to the nearest cubic foot.)
QUESTION 2:
The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss, at various temperatures in degrees Celsius:
Temperature(oC)(oC) | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
Percent heat loss from beak | 36 | 36 | 32 | 36 | 33 | 44 | 52 | 51 | 40 | 54 | 44 | 51 | 63 | 56 | 65 | 66 |
The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is
yˆ=y^= + x
(Use decimal notation. Give your answer to four decimal places.)
Use the equation to predict (±0.01)(±0.01) beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 25 degrees Celsius.
%
What percent (±0.01)(±0.01) of the variation in beak heat loss is explained by the straight-line relationship with temperature?
%
Find the correlation rr (±± 0.001) between beak heat loss and temperature:
r=
In: Statistics and Probability
Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims. Suppose a random sample of employees gave the following information. x 2 8 14 32 73 y 50 45 35 28 16 Given that the value of r is -0.949, should y increase as x increases, does the value of r imply that y should tend to increase, decrease, or remain the same? Explain.
In: Statistics and Probability
A random sample of the price of gasoline from 30 gas stations in a region gives the statistics below. Complete parts a through c below.
y= $3.89, SE (y) =$0.06
a) Find a 95% confidence interval for the mean price of regular gasoline in that region.
(Round to three decimal places as needed.)
b) Find the 90% confidence interval for the mean.
(Round to three decimal places as needed.)
c) If we had the same statistics from a sample of 60stations, what would the 95% confidence interval be now?
(Round to three decimal places as needed.)
In: Statistics and Probability
An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via "smart phones", so they want to estimate the proportion of users who access the site that way (even if they also use their computers sometimes). They draw a random sample of
200200
investors from their customers. Suppose that the true proportion of smart phone users is
3737%.
a) What would the standard deviation of the sampling distribution of the proportion of the smart phone users be?
. 034.034
(Round to three decimal places as needed.)
b) What is the probability that the sample proportion of smart phone users is greater than
0.370.37?
. 5.5
(Round to three decimal places as needed.)
c) What is the probability that the sample proportion is between
0.320.32
and
0.420.42?
. 858.858
(Round to three decimal places as needed.)
d) What is the probability that the sample proportion is less than
0.300.30?
. 02.02
(Round to three decimal places as needed.)
e) What is the probability that the sample proportion is greater than
0.440.44?
______
(Round to three decimal places as needed.)
In: Statistics and Probability
There are two urns, urn I and urn II. Urn I contains 2 white
balls and 4 red balls, and urn II
contains 1 white ball and 1 red ball. A ball is randomly chosen
from urn I and put into urn II,
and a ball is then randomly selected from urn II. What is the
probability that the ball selected
from urn II is white?
In: Statistics and Probability