If we have 8 categories and we are testing whether the data is uniformly distributed (equally...
Homework Answers
Number of categories = 8
Sample size = 120
The expected value of each cell would be 120/8 = 15
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If we have 8 categories and we are testing whether the data is
uniformly distributed (equally...
1.) A variable contains seven categories. It is expected that data are uniformly distributed across these...
1.) A variable contains seven categories. It is expected that data are uniformly distributed across these seven categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, 18, 33 and 24. What is the value of test statistic equals to, using a significance level of 1%? a. a. 18.475 b. b. 10.645 c. c. 6.46 d. d. 0.374
A variable contains five categories. It is expected that data are uniformly distributed across these five...
A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using α = .01, the degrees of freedom for this test are ___. 5 4 3 2 1
A variable contains five categories. It is expected that data are uniformly distributed across these five...
A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30 29, 21, and 24. Using a = .01, the appropriate decision is - O reject the null hypothesis that the observed distribution is uniform reject the null hypothesis that the observed distribution is not uniform O do not reject the null hypothesis that the...
The difference of two independent normally distributed random variables is also normally distributed. We have used...
The difference of two independent normally distributed random
variables is also normally distributed. We have used this fact in
many of our derivations. Now, consider two independent and normally
distributed populations with unknown variances σ 2 X and σ 2 Y . If
we get a random sample X1, X2, . . . , Xn from the first population
and a random sample Y1, Y2, . . . , Yn from the second population
(note that both samples are of...
Suppose you have an unbiased, normally distributed estimator of a parameter B, and are testing the...
Suppose you have an unbiased, normally distributed estimator of a parameter B, and are testing the null hypothesis B=0 with a two tail test. For the present sample, the standard error of the estimator is 1.0 Suppose the true value of B=0.5. Professor X conducts the study and finds a positive and significant B. If you attempt to replicate Professor X's study in other data sets of the same size, what percentage of those data sets would you expect the...
Worksheet: Chi Square and Correlation Suppose we have three categories A, B, and C. Assume that...
Worksheet: Chi Square and Correlation Suppose we have three categories A, B, and C. Assume that the historical distribution of observations among these four categories is 20%, 40%, and 40% respectively. A sample of size 250 is taken, and we find 75 observations in category A, 125 in category B, and 50 in category C 1. a. State the null hypothesis for the Chi-square goodness-of-fit test. b. What are the expected frequencies for each category? c. Calculate the χ 2...
10.36 A consumer testing organization wants to know whether two brands of work shoes have equally...
10.36 A consumer testing organization wants to know whether two brands of work shoes have equally long-lasting heels. Tests show that 50 randomly selected workers wore out the heels of Brand X shoes, on average, in 96 days with a standard deviation of 6.4 days, while 50 randomly selected workers wore out the heels of Brand Y shoes, on average, in 99 days with a standard deviation of 6.1 days. (a) Test at the level of significance a = 0.05...
You are conducting a multinomial hypothesis test (α = 0.05) for the claim that all 5...
You are conducting a multinomial hypothesis test (α = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table. Category Observed Frequency Expected Frequency A 10 B 5 C 21 D 14 E 8 What is the chi-square test-statistic for this data? χ2= What are the degrees of freedom for this test? d.f.= What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = Is the P-Value... A....
7. We want to conduct a survey using professors at a university. We divide them into...
7. We want to conduct a survey using professors at a university. We divide them into the categories of instructor, associate professor, and full professor, and take a sample of size 20 from each category.:* Oa. Simple Random Sample Ob. Systematic Oc. Stratified Od. Cluster Oe. Convenience 8. Now we pass by the science department and come across a group of science professors talking in a classroom. We decide to use this group as our study sample.: Oa. Simple Random...
.. We are interested in testing whether or not a coin is balanced based on the...
.. We are interested in testing whether or not a coin is balanced based on the number of heads Y on 36 tosses of the coin (Ho : p = 0.5 versus HA : P = 0.5). Suppose we use the rejection region {y: ly - 181 > 4}. (a) In terms of this problem what would be a type I and type II error? (b) Find the level, a, of the test. (Hint: Is a Normal approximation appropriate?) (c)...
A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30 29, 21, and 24. Using a = .01, the appropriate decision is - O reject the null hypothesis that the observed distribution is uniform reject the null hypothesis that the observed distribution is not uniform O do not reject the null hypothesis that the...
The difference of two independent normally distributed random
variables is also normally distributed. We have used this fact in
many of our derivations. Now, consider two independent and normally
distributed populations with unknown variances σ 2 X and σ 2 Y . If
we get a random sample X1, X2, . . . , Xn from the first population
and a random sample Y1, Y2, . . . , Yn from the second population
(note that both samples are of...
Worksheet: Chi Square and Correlation Suppose we have three categories A, B, and C. Assume that the historical distribution of observations among these four categories is 20%, 40%, and 40% respectively. A sample of size 250 is taken, and we find 75 observations in category A, 125 in category B, and 50 in category C 1. a. State the null hypothesis for the Chi-square goodness-of-fit test. b. What are the expected frequencies for each category? c. Calculate the χ 2...
10.36 A consumer testing organization wants to know whether two brands of work shoes have equally long-lasting heels. Tests show that 50 randomly selected workers wore out the heels of Brand X shoes, on average, in 96 days with a standard deviation of 6.4 days, while 50 randomly selected workers wore out the heels of Brand Y shoes, on average, in 99 days with a standard deviation of 6.1 days. (a) Test at the level of significance a = 0.05...
7. We want to conduct a survey using professors at a university. We divide them into the categories of instructor, associate professor, and full professor, and take a sample of size 20 from each category.:* Oa. Simple Random Sample Ob. Systematic Oc. Stratified Od. Cluster Oe. Convenience 8. Now we pass by the science department and come across a group of science professors talking in a classroom. We decide to use this group as our study sample.: Oa. Simple Random...
.. We are interested in testing whether or not a coin is balanced based on the number of heads Y on 36 tosses of the coin (Ho : p = 0.5 versus HA : P = 0.5). Suppose we use the rejection region {y: ly - 181 > 4}. (a) In terms of this problem what would be a type I and type II error? (b) Find the level, a, of the test. (Hint: Is a Normal approximation appropriate?) (c)...
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