In a televised game show, contestants are asked to pick what is behind Door #1,

Question

In a televised game show, contestants are asked to pick what is behind Door #1, Door #2, Door #3, and Door #4. The only difference the contestant can see is the number on the door. If contestants do not have a preference for particular numbers, then each door should have a 25% chance of being selected. The game producers, however, have decided to analyze the contestant’s choices to see if they have a preference for certain doors, so they gathered the following data on door choices: out of 160 trials, contestants made the following choices: Door #1 was selected 38 times; Door #2 was selected 42 times; Door #3 was selected 42 times; Door number 4 was selected 38 times. Using a Chi Square Test for Goodness of Fit, would we reject or fail to reject a null hypothesis that Door Selection is uniform over the numbers one through four?

Question 11 options:

In a televised game show, contestants are asked to pick what is behind Door #1, Door #2, Door #3, and Door #4. The only difference the contestant can see is the number on the door. If contestants do not have a preference for particular numbers, then each door should have a 25% chance of being selected. The game producers, however, have decided to analyze the contestant’s choices to see if they have a preference for certain doors, so they gathered the following data on door choices: out of 160 trials, contestants made the following choices: Door #1 was selected 25 times; Door #2 was selected 60 times; Door #3 was selected 55 times; Door number 4 was selected 20 times. . Using a Chi Square Test for Goodness of Fit, would we reject or fail to reject a null hypothesis that Door Selection is uniform over the numbers one through four?

Question 14 options:

The chi-square distribution is a skewed distribution whose mean value is n-1 for df > 2.

Question 3 options:

Which of the following are true regarding a Chi-Square Test for Homogeneity?
I. May be used to test the claim that several proportions are equal when samples are taken from different populations
II. After sampling several populations for the same characteristic, we test whether the proportions in each category are the same
III. The Chi-Square Test for Homogeneity uses the same techniques as for the chi-square tests for independence
IV. Ho: The proportions are not equal

Question 12 options:

a) The p-value is high, indicating that if the door choices were uniform, we would expect to see the chi-square value occur over 90% of the time. This certainly is not unusual, so I fail to reject the null hypothesis and conclude that the data shows virtually no evidence of non-uniform distribution of Door Selection among the contestants. b) The p-value is high, indicating that if the door choices were uniform, we would expect to see the chi-square value occur over 90% of the time. This certainly is not unusual, so I reject the null hypothesis and conclude that the data shows evidence of non-uniform distribution of Door Selection among the contestants. c) The p-value is low, indicating that if the door choices were uniform, we would not expect to see the chi-square value occur over 90% of the time. This certainly is not unusual, so I fail to reject the null hypothesis and conclude that the data shows virtually no evidence of non-uniform distribution of Door Selection among the contestants. d) The p-value is low, indicating that if the door choices were uniform, we would expect to see the chi-square value occur over 90% of the time. This certainly is not unusual, so I reject the null hypothesis and conclude that the data shows evidence of non-uniform distribution of Door Selection among the contestants. e) None of the above is correct.

Explanation / Answer

Solving question 1, please repost rest individually.

The Chi^2 value is: 0.4

The Chi^2 value is 0.4. The P-Value is 0.94. The result is not significant at p=0.05.

Hence, the correct answer is A.

Observed Expected Difference Difference Sq. Diff. Sq. / Exp Fr. a 38 40   -2.00   4.00   0.10 b 42 40   2.00   4.00   0.10 c 42 40   2.00   4.00   0.10 d 38 40   -2.00   4.00   0.10   0.400

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