Questions
13 Balls are in an urn. 4 are blue, 3 are black, 6 are red. If...

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...

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...

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

The mean monthly mortage payment for homwowners in the local community was $2365, and the standard...

The mean monthly mortage payment for homwowners in the local community was $2365, and the standard deviation was $340. Using Chebyshev’s therorem, calculate the percentage of homeowners in this town who pay between $1685 and $3045.

In: Statistics and Probability

The total cholesterol levels of a sample of men aged​ 35-44 are normally distributed with a...

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...

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%...

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...

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...

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...

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...

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...

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...

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 60​stations, 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...

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...

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