Question

A researcher is interested in voting preferences on change of the governing constitution in a certain country controlled by two main parties A and B. A questionnaire was developed and sent to a random sample of voters. The cross tabs are as follows Favour Neutral Oppose Membership: Party A 70 90 85 Party B 50 50 155 Test at α = 0.05 whether party membership and voting preference are associated and state the conditions required for chi-square test results to be valid.

288

likes
1440 views

Answer to a math question A researcher is interested in voting preferences on change of the governing constitution in a certain country controlled by two main parties A and B. A questionnaire was developed and sent to a random sample of voters. The cross tabs are as follows Favour Neutral Oppose Membership: Party A 70 90 85 Party B 50 50 155 Test at α = 0.05 whether party membership and voting preference are associated and state the conditions required for chi-square test results to be valid.

Expert avatar
Clarabelle
4.7
94 Answers
To test whether party membership and voting preference are associated, we can use a chi-square test of independence. The null hypothesis (H0) is that there is no association between party membership and voting preference, while the alternative hypothesis (H1) is that there is an association. The observed values for the cross tabs are as follows: Favour Neutral Oppose Party A 70 90 85 Party B 50 50 155 To perform the chi-square test, we need to calculate the expected values under the assumption of independence. The expected values can be obtained by assuming that party membership and voting preference are independent and calculating the expected counts based on the row and column totals. The expected values are as follows: Favour Neutral Oppose Party A 58.33 58.33 128.34 Party B 61.67 61.67 135.66 Now, we can set up the chi-square test: 1. Set the significance level (α) to 0.05. 2. Calculate the degrees of freedom (df) as (number of rows - 1) * (number of columns - 1). In this case, df = (2-1) * (3-1) = 2. 3. Calculate the chi-square test statistic using the formula: χ^2 = Σ [(O - E)^2 / E], where Σ represents the sum of the cells, O is the observed value, and E is the expected value. 4. Compare the calculated chi-square test statistic with the critical chi-square value from the chi-square distribution table with the given degrees of freedom and significance level. 5. If the calculated chi-square test statistic is greater than the critical chi-square value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis. Performing the calculations, we obtain a chi-square test statistic of approximately 22.88. Looking up the critical chi-square value with 2 degrees of freedom and a significance level of 0.05, we find a critical chi-square value of approximately 5.99. Since the calculated chi-square test statistic (22.88) is higher than the critical chi-square value (5.99), we reject the null hypothesis. Therefore, we can conclude that there is evidence to suggest an association between party membership and voting preference in this country. Conditions required for the chi-square test results to be valid: 1. Random sampling: The sample of voters should be randomly selected to ensure representativeness. 2. Independence: The observations in the cross tabs should be independent of each other. 3. Sufficient sample size: The expected count for each cell in the cross tabs should be at least 5. If not, the chi-square test may not be valid, and alternative methods should be considered.

Frequently asked questions (FAQs)
Question: What is the value of (2^3)^2 - √144 + 5^2?
+
How many ways can a committee of 4 people be selected from a group of 10, where the order does not matter?
+
What is the equation of the exponential function y = e^(0.07x) when graphed?
+
New questions in Mathematics
a runner wants to build endurance by running 9 mph for 20 min. How far will the runner travel in that time period?
X^2 = 25
(-5/6)-(-5/4)
Identify a pattern in the list of numbers.Then use this pattern to find the next number. 37,31,25,19,13
A National Solidarity Bond offers A 5 year bond offering a gross return of 15% Calculate the AER for this investment. (Give your answer to two decimal places, no need for the percent or € sign in your answer)
I want you to solve this problem as a grade sixth pupil in primary school: 8 Pigs ate 6 bags of fee in 20 days. How long will it take 10 pigs to eat 15 bags of feed eating at the same rate?
User Before the election, a poll of 60 voters found the proportion who support the Green candidate to be 25%. Calculate the 90% confidence interval for the population parameter. (Give your answers as a PERCENTAGE rounded to TWO DECIMAL PLACES: exclude any trailing zeros and DO NOT INSERT THE % SIGN) Give the lower limit of the 90% confidence interval Give the upper limit of the 90% confidence interval
Given (3x+2)E [2;14] how much money (in soles) does Sophia have if numerically it is the greatest value of x?
The market for economics textbooks is represented by the following supply and demand equations: P = 5 + 2Qs P = 20 - Qd Where P is the price in £s and Qs and Qd are the quantities supplied and demanded in thousands. What is the equilibrium price?
Use a pattern to prove that (-2)-(-3)=1
9 x² + 2x + 1 = 0
The volume of a cube decreases at a rate of 10 m3/s. Find the rate at which the side of the cube changes when the side of the cube is 2 m.
A,B,C and D are the corners of a rectangular building. Find the lengths the diagonals if AB measures 38' - 9" and AD measures 56' - 3"
A hardware bill totals $857.63 with discounts of 5% and 3%. What is the net cost of the Material ?
viii. An ac circuit with a 80 μF capacitor in series with a coil of resistance 16Ω and inductance 160mH is connected to a 100V, 100 Hz supply is shown below. Calculate 7. the inductive reactance 8. the capacitive reactance 9. the circuit impedance and V-I phase angle θ 10. the circuit current I 11. the phasor voltages VR, VL, VC and VS 12. the resonance circuit frequency Also construct a fully labeled and appropriately ‘scaled’ voltage phasor diagram.
A buyer purchased a North Carolina home for $475,250. The seller allowed the buyer to assume his first small mortgage with a loan balance of $110,000. How much is the excise tax paid in the transaction? $951 $729.50 $950.50 $221 none of the above
00 piece jigsaw puzzle. the completed puzzle is 10x10. each piech connects to at least 2 other pieces. i plan to assemble by taking pieces out of box one by one. if i've already taken out 2 pieces that dont directly connect, what is the minimum number of additional pieces that i need to draw to in order to guarentee that the original 2 pieces connect?
solve R the following equation 4 x squared - 35 - 9 over x squared is equal to 0
y′ = 2x + 3y x′ = 7x − 4y x(0) = 2 y(0) = −1 sisteminin ¸c¨oz¨um¨un¨u bulunuz. (Lineer Denk. Sis.)
In an experiment to assess the effect of listening to audiobooks while driving, participants were asked to drive down a straight road in a driving simulator. The accompanying data on time (in milliseconds) to react when a pedestrian walked into the street for 10 drivers listening to an audiobook are consistent with summary statistics and graphs that appeared in the paper "Good Distractions: Testing the Effect of Listening to an Audiobook on Driving Performance in Simple and Complex Road Environments."† (Round your answers to four decimal places.) 1,018 1,007 1,054 988 937 1,030 1,065 1,011 860 1,106 A button hyperlink to the SALT program that reads: Use SALT. Calculate the variance for this data set. 7437.7333 Incorrect: Your answer is incorrect. Calculate the standard deviation for this data set. 86.2022 Incorrect: Your answer is incorrect.