Question

In: Statistics and Probability

The national distribution of fatal work injuries in a country is shown in the table to...

The national distribution of fatal work injuries in a country is shown in the table to the right under National ​%. You believe that the distribution of fatal work injuries is different in the western part of the country and randomly select 6231 fatal work injuries occurring in that region. At alpha equals 0.05 can you conclude that the distribution of fatal work injuries in the west is different from the national​ distribution? Complete parts a through d below. Cause National​ % Western Frequency Transportation 43​% 2893 Equipment 19​% 1162 Assaults 15​% 805 Falls 13​% 749 Harmful fumes 7​% 531 Fires 3​% 91

a. State Upper H 0 and Upper H Subscript a and identify the claim. What is the null​ hypothesis, Upper H 0​? A. The distribution of fatal work injuries in the west differs from the expected distribution. B. The distribution of fatal work injuries in the west is 43​% ​transportation, 19​% ​equipment, 15 % ​assaults, 13​% ​falls, 7​% harmful​ fumes, and 3​% fires. C. The distribution of fatal work injuries in the west is 2893 ​transportation, 1162 ​equipment, 805 ​assaults, 749 ​falls, 531 harmful​ fumes, and 91 fires. What is the alternate​ hypothesis, Upper H Subscript a​? A. The distribution of fatal work injuries in the west is the same as the expected distribution. B. The distribution of fatal work injuries in the west is 43​% ​transportation, 19​% ​equipment, 15 % ​assaults, 13​% ​falls, 7​% harmful​ fumes, and 3​% fires. C. The distribution of fatal work injuries in the west differs from the expected distribution.

Which hypothesis is the​ claim? Upper H 0 Upper H Subscript a

b. Determine the critical​ value, font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2​, and the rejection region. font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2equals nothing ​(Round to three decimal places as​ needed.)

Determine the rejection region. A. font size increased by 1 font size increased by 1 font size increased by 1 chi squared greater than font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2 B. font size increased by 1 font size increased by 1 font size increased by 1 chi squared less than or equals font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2 C. font size increased by 1 font size increased by 1 font size increased by 1 chi squared greater than or equals font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2 D. font size increased by 1 font size increased by 1 font size increased by 1 chi squared less than font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2

c. Calculate the test statistic. font size increased by 1 font size increased by 1 font size increased by 1 chi squaredequals nothing ​(Round to three decimal places as​ needed.) ​

(d) Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. Reject Reject Fail to reject Upper H 0. At the 5​% significance​ level, there is is is not enough evidence to conclude that the western distribution of fatal work injuries differs from differs from is the same as the national distribution.

Solutions

Expert Solution

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: B) The distribution of fatal work injuries in the west is 43​% ​transportation, 19​% ​equipment, 15 % ​assaults, 13​% ​falls, 7​% harmful​ fumes, and 3​% fires.
Alternative hypothesis: C) The distribution of fatal work injuries in the west differs from the expected distribution.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = k - 1 = 6 - 1
D.F = 5
(Ei) = n * pi

X2 = 109.87

X2Critical = 11.07

Rejection region is X2 > 11.07

where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, Ei is the expected frequency count for level i, Oi is the observed frequency count for level i, and X2 is the chi-square test statistic.

Interpret results. Since the X2-value lies in the rejection region, hence we have to reject the null hypothesis.

Reject H0. At the 5​% significance​ level, there is is enough evidence to conclude that the western distribution of fatal work injuries differs from the national distribution.

orchestra answered 2 years ago
Next > < Previous

Related Solutions

The national distribution of fatal work injuries in a country is shown in the table to...
The national distribution of fatal work injuries in a country is shown in the table to the right under National %. You believe that the distribution of fatal work injuries is different in the western part of the country and randomly select 5000 fatal work injuries occurring in that region. At α= 0.10, can you conclude that the distribution of fatal work injuries in the west is different from the national​ distribution? % Actual counts Category 1 20% 1020 Category...
The national distribution of fatal work injuries in a country is shown in the table to...
The national distribution of fatal work injuries in a country is shown in the table to the right under National ​%. You believe that the distribution of fatal work injuries is different in the western part of the country and randomly select 6231 fatal work injuries occurring in that region. At alpha equals 0.10α=0.10 can you conclude that the distribution of fatal work injuries in the west is different from the national​ distribution? Complete parts a through d below. calculate...
following data safety injury severity Fatal non-fatal no injuries total yes 669 155,071 467,362 623,102 no...
following data safety injury severity Fatal non-fatal no injuries total yes 669 155,071 467,362 623,102 no 487 4294 3824 8605 total 1,156 159,365 471,186 631,707 using this data, we wish to determine if there is any association between using safety restraints and injury severity. as such we will use a chi-square test for independence Q10: state the null and alternative hypotheses Q11:fill in the table below with the expected counts assuming the null hypothesis is true safety restraint/injury severity fatal...
How old are college students? The national age distribution for the youth is shown below.       ...
How old are college students? The national age distribution for the youth is shown below.        National Age Distribution for the college Age Under 26 26–35 36–45 46–55 Over 55 Percentage 39% 25% 16% 12% 8% The Mountain Colleges took a random sample of 212 students and obtained the following sample distribution.        Sample Distribution, Mountain Colleges Age Under 26 26–35 36–45 46–55 Over 55 Number of students 65 73 41 21 12        Is the sample age distribution for the  ...
Activity 1: National records have shown that the distribution of time lengths (in years) needed to...
Activity 1: National records have shown that the distribution of time lengths (in years) needed to complete a bachelor's degree is approximately bell-shaped (normal) where the mean is 4.6 yrs and the standard deviation is .3 years. 1C. Would you expect someone to take more than 6 years to complete a bachelor’s degree? 1D. What percent of college students take at most 4.3 years? 1E. What percent of college students take at least 5.2 years? 1F. What percent of students...
Table 2 below shows the national income accounting data for the year 2020 in Country A....
Table 2 below shows the national income accounting data for the year 2020 in Country A. Using expenditure approach, calculate the following values: Items RM (Million) Depreciation 560 Gross private domestic investment expenditures 5980 Imports 9900 Exports 3000 Federal government expenditures 7900 State and local government expenditures 1653 Personal consumption expenditure 8960 Transfer payments 300 Receipts of factor income from the rest of the world 930 Payments of factor income to the rest of the world 1890 (i) Gross domestic...
The joint probability distribution of random variables, X and Y, is shown in the following table:...
The joint probability distribution of random variables, X and Y, is shown in the following table: X 2 4 6 Y 1 0.10 0.20 0.08 2 0.06 0.12 0.16 3 0.15 0.04 0.09 (a) Calculate P ( X=4 | Y=1) (b) Calculate V (Y | X=2) . (c) Calculate V (3Y-X ) .
Consider the population described by the probability distribution shown in the table. The random variable x...
Consider the population described by the probability distribution shown in the table. The random variable x is observed twice. If these observations are independent, all the different samples of size 2 and their probabilities are shown in the accompanying table. Complete parts a through e below. x 1 2 3 4 5 p(x) 0.4 0.1 0.2 0.2 0.1 x (bar over x) 1.0 1.5 2.0 2.5 3 3.5 4 4.5 5 p(x) (bar over x) 0.16 0.08 0.17 0.2 0.16...
The joint probability distribution of variables X and Y is shown in the table below. ...............................................................................X..........................................................................
The joint probability distribution of variables X and Y is shown in the table below. ...............................................................................X....................................................................... Y 1 2 3 1 0.30 0.18 0.12 2 0.15 0.09 0.06 3 0.05 0.03 0.02 Calculate E(XY) Determine the marginal probability distributions of X and Y.             Calculate E(X) and E(Y)             Calculate V(X) and V(Y)             Are X and Y independent? Explain.             Find P(Y = 2| X = 1) Calculate COV(X,Y). Did you expect this answer? Why? Find the probability distribution...
The frequency distribution shown in the following table lists the number of hours per day a...
The frequency distribution shown in the following table lists the number of hours per day a randomly selected sample of teenagers spent watching television. Where possible, determine what percent of the teenagers spent the following number of hours watching television. (Round your answers to one decimal place. If not possible, enter IMPOSSIBLE.) Hours per day Number of Teenagers 0 ≤ x < 1 17 1 ≤ x < 2 31 2 ≤ x < 3 24 3 ≤ x <...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT