For Problems 3–11, please provide the following information.
- (a) What is the level of significance? State the null and alternate hypotheses.
- (b) Find the value of the chi-square statistic for the sample. What are the degrees of freedom? What assumptions are you making about the original distribution?
- (c) Find or estimate the P-value of the sample test statistic.
- (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?
- (e) Interpret your conclusion in the context of the application.
- (f) Find the requested confidence interval for the population variance or population standard deviation. Interpret the results in the context of the application.
In each of the following problems, assume a
Law: Bar Exam A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between “better,” “average,” and “poorer” students. A group of attorneys in a Midwest state has been given the task of making up this year’s bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 24 newly graduated law students. Their scores give a sample standard deviation of 72 points.
- (i) Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60.
- (ii) Find a 99% confidence interval for the population variance.
- (iii) Find a 99% confidence interval for the population standard deviation.
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Understandable Statistics: Concepts and Methods
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- In the picture there is a given data and based from that data. There is no significant difference between the perceived level of riskiness of thrill behavior in males and in females. (Use a= 0.05) Identify the Null hypothesis and Alternative Hypothesisarrow_forwardFor each of the following investigations, state i) null hypothesis, ii) alternative hypothesis and iii) type of test, two sided/one sided. a) You wish to investigate if income from tobacco farming is greater than that of from tea farming in Malawi. b) You want to compare proportion of army worms killed by Doom those killed by Attack pesticide.arrow_forwardThe closer the numerator of a t-test gets to zero, the more likely it is that there is no statistically significant difference between the two means we are testing. True Falsearrow_forward
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