11.29 The following table gives the distributions of grades for three professors for a few randomly selected classes that each of them taught during the last 2 years Professor Miller Smith Мoore 18 36 20 25 15 44 Grade 73 85 82 D and F 17 12 8 Using a 2.5% significance level, test the null hypothesis that the grade distributions are homogeneous for these three professors AB
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- The following data show the number of class sessions missed during a semester of SOC221 and the final grade for a sample of 8 students selected at random. Number of Sessions Missed Final Grade (x) (y) 0 96 2 88 12 68 6 91 8…31% of all pygmy softshell toises have stripes on their shells. A herpetologist in Cititon collects a sample of 28 pygmy softshell tortoises and finds that 8 of them have stripes on their shells. Is there enough evidence to conclude, at a significance of alpha=0.05, that the proportion of pygmy softshell tortoises in Cititon with stripes on their shells is less than 31%? What is the claim? What is the null hypothesis? What is the alternative hypothesis? What is the test statistic? What is/are the critical value(s)? Do we reject the null hypothesis? What conclusion do we draw? What is the P-value for the problem above?A sample of men and women who had passed their driver's test either the first time or the second time were surveyed, with the following results: Results of the driving testGender First time Second timeMen 126 211Women 135 178a) Do these data suggest that there is a relationship between gender and the passing of their driver’s test from which the present sample was drawn? Let alpha=.05
- Suppose that we want to investigate whether on the average men earn more than women in a certain industry. If a sample data show that the 60 men earn on an average $292.50 per week with a SD $ 15.60, while 60 women earn on an average $266.10 per week with a SD $ 18.20, what can we conclude at the 0.01 level of significance?The number of contaminating particles on a silicon waferprior to a certain rinsing process was determined for eachwafer in a sample of size 100, resulting in the followingfrequencies:Number of particles 0 1 2 3 4 5 6 7Frequency 1 2 3 12 11 15 18 10Number of particles 8 9 10 11 12 13 14Frequency 12 4 5 3 1 2 1a. What proportion of the sampled wafers had at leastone particle? At least five particles?b. What proportion of the sampled wafers had betweenfive and ten particles, inclusive? Strictly between fiveand ten particles?c. Draw a histogram using relative frequency on thevertical axis. How would you describe the shape of thehistogram?Two samples of n = 5 participants each generate the following data. Calculate a t-test score for the difference of these two groups. Group 1 Group 2 2 3 3 3 2 2 2 2 1 2 t(8) = 2.86 t(8) = 2.29 t(8) = 2.5 t(8) = 1.11 Based on the results from the previous question (#7), what is the tcrit and are Group 1 and Group 2 significantly different from each other? Use α = .05, two-tailed test. tcrit = 1.860 Yes, the two groups are significantly different from each other. tcrit = 2.306 Yes, the two groups are significantly different from each other. tcrit = 2.228 Yes, the two groups are significantly different from each other. tcrit = 3.355 No, the two groups are not significantly different from each other.
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