Question

In: Statistics and Probability

Question 1- A graphing calculator is recommended. Are the mean number of times a month a...

Question 1-

A graphing calculator is recommended.

Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Suppose that the table below shows the results of a study.

White Black Hispanic Asian
5 3 8 7
8 1 3 3
2 5 5 5
4 2 4 1
6 6 7

Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05. (Let 1 = White, 2 = Black, 3 = Hispanic, and 4 = Asian.)

1) Enter an exact number as an integer, fraction, or decimal.

df(num) =

2)Enter an exact number as an integer, fraction, or decimal.

df(denom) =

3)What is the test statistic? (Round your answer to two decimal places.)

4) What is the p-value? (Round your answer to four decimal places.)

5)  Alpha (Enter an exact number as an integer, fraction, or decimal.)

α =

Question 2-College students may be interested in whether or not their majors have any effect on starting salaries after graduation. Suppose that 298 recent graduates were surveyed as to their majors in college and their starting salaries after graduation. Below are the data. Conduct a test of independence. (Use a significance level of 0.05.)

Major < $50,000 $50,000 - $68,999 $69,000 +
English 4 20 4
Engineering 10 30 61
Nursing 10 16 14
Business 9 20 31
Psychology 19 29 21

1) What is the test statistic? (Round your answer to two decimal places.)

2) Alpha (Enter an exact number as an integer, fraction, or decimal.)
α =  

Solutions

Expert Solution

A B C D
count, ni = 5 4 5 5
mean , x̅ i = 5.000 2.75 5.20 4.60
std. dev., si = 2.236 1.708 1.924 2.61
sample variances, si^2 = 5.000 2.917 3.700 6.800
total sum 25 11 26 23 85 (grand sum)
grand mean , x̅̅ = Σni*x̅i/Σni =   4.47
square of deviation of sample mean from grand mean,( x̅ - x̅̅)² 0.277 2.971 0.528 0.016
TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² = 1.385 11.884 2.638 0.080 15.98684
SS(within ) = SSW = Σ(n-1)s² = 20.000 8.750 14.800 27.200 70.7500

no. of treatment , k =   4
df between = k-1 =    3
N = Σn =   19
df within = N-k =   15
  
mean square between groups , MSB = SSB/k-1 =    5.3289
  
mean square within groups , MSW = SSW/N-k =    4.7167
  
F-stat = MSB/MSW =    1.13

anova table
SS df MS F p-value F-critical
Between: 15.99 3 5.33 1.13 0.3686 3.29
Within: 70.75 15 4.72
Total: 86.74 18
α = 0.05
conclusion : p-value>α , do not reject null hypothesis    

P VALUE = 0.3686

ALPHA = 0.05

...................

2)

Observed Frequencies
0
0 <50000 50000-68999 69000+ Total
ENG 4 20 4 28
ENGGRNG 10 30 61 101
NURSING 10 16 14 40
BUSINESS 9 20 31 60
PSYCHOLOGY 19 29 21 69
Total 52 115 131 298
Expected frequency of a cell = sum of row*sum of column / total sum
Expected Frequencies
<50000 50000-68999 69000+ Total
ENG 52*28/298=4.886 115*28/298=10.805 131*28/298=12.309 28
ENGGRNG 52*101/298=17.624 115*101/298=38.977 131*101/298=44.399 101
NURSING 52*40/298=6.98 115*40/298=15.436 131*40/298=17.584 40
BUSINESS 52*60/298=10.47 115*60/298=23.154 131*60/298=26.376 60
PSYCHOLOGY 52*69/298=12.04 115*69/298=26.628 131*69/298=30.332 69
Total 52 115 131 298
(fo-fe)^2/fe
ENG 0.161 7.824 5.609
ENGGRNG 3.298 2.067 6.207
NURSING 1.3068 0.0206 0.7305
BUSINESS 0.2063 0.4297 0.8107
PSYCHOLOGY 4.0230 0.2114 2.8712

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   35.78  
      
Level of Significance =   0.05  
Number of Rows =   5  
Number of Columns =   3  
Degrees of Freedom=(#row - 1)(#column -1) = (5- 1 ) * ( 3- 1 ) =   8  
      
p-Value =   0.0000   [Excel function: =CHISQ.DIST.RT(χ²,df) ]
Decision:    p-value < α , Reject Ho  

..................


THANKS

revert back for doubt

please upvote


Related Solutions

A graphing calculator is recommended. Solve the following exercise on a graphing calculator by graphing an...
A graphing calculator is recommended. Solve the following exercise on a graphing calculator by graphing an appropriate exponential function (using x for ease of entry) together with a constant function and using INTERSECT to find where they meet. You will have to choose an appropriate window. (Round your answers to one decimal place.) At 3% inflation, prices increase by 3% compounded annually. (a) How soon will prices double?   yr (b) How soon will prices triple?   yr
A graphing calculator is recommended. For the limit lim x → 2 (x3 − 3x +...
A graphing calculator is recommended. For the limit lim x → 2 (x3 − 3x + 8) = 10 illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1. (Round your answers to four decimal places.) ε = 0.2     δ = ε = 0.1     δ =
A graphing calculator is recommended. For the limit lim x → 2 (x3 − 2x +...
A graphing calculator is recommended. For the limit lim x → 2 (x3 − 2x + 4) = 8 illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1. (Round your answers to four decimal places.) ε = 0.2     δ =   ε = 0.1     δ =
A graphing calculator is recommended. Three students, Linda, Tuan, and Javier, are given five laboratory rats...
A graphing calculator is recommended. Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypothesis that the three...
Are the mean number of times a month a person eats out the same for whites,...
Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? White Black Hispanic Asian 6 4 7 8 8 1 3 3 2 5 5 5 4 2 4 1 6 6 7 df numerator and denominator = Write Ho and Ha What is the p-value? Do you reject or accept the null hypothesis at the 5% level?
Please solve using graphing calculator. Include what is typed into calculator in your explaination. For example:...
Please solve using graphing calculator. Include what is typed into calculator in your explaination. For example: First, type the data under L1, then go to STAT --> TESTS -->TInverval. Inpt: Data (highlight the word Data) List: L1 Freq: 1 C-level .98 Calculate--> (3.54, 4.29) Show as much work as you can to support answer. In a Pew Research Center poll 745 randomly selected adults, 589 said that it is morally wrong not to report all income on tax returns. Assume...
How to Factor Polynomials on a Graphing Calculator (TI-83 and TI-84)
How to Factor Polynomials on a Graphing Calculator (TI-83 and TI-84)
Using either logarithms or a graphing​ calculator, find the time required for ​$5000 to be at...
Using either logarithms or a graphing​ calculator, find the time required for ​$5000 to be at least equal to ​$9000 when deposited at 5 ​% compounded monthly.
Use your graphing calculator to find the solutions to the following equation for 0° ≤ θ...
Use your graphing calculator to find the solutions to the following equation for 0° ≤ θ < 360° by defining the left side and right side of the equation as functions and then finding the intersection points of their graphs. Make sure your calculator is set to degree mode. (Round your answers to one decimal place. Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 3 sin2 θ + 1 = 5 sin θ
Define the random variable X to be the number of times in the month of June...
Define the random variable X to be the number of times in the month of June (which has 30 days) Susan wakes up before 6am a. X fits binomial distribution, X-B(n,p). What are the values of n and p? c. what is the probability that Susan wakes us up before 6 am 5 or fewer days in June? d. what is the probability that Susan wakes up before 6am more than 12 times?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT