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Hypothesis Testing (For t distribution- single sample) Question 12.1 a. A random sample of 25 was drawn from a population. The sample mean and standard deviation are x = 510 and s = 125. Estimate with 95% confidence. Hypothesis Testing (For population- single sample) Question 12.54 a. In a random sample of 500 observations, we found the proportion of successes to be 48%. Estimate with 95% confidence the population proportion of successes. Hypothesis Testing (For z distribution –two sample) Question 13.1 In random sample of 25 from each of two normal populations, we found the following statistics: x 1 = 524 x 2 = 469 s1 = 129 s2 = 131 a. Estimate the difference between the two populations means with 95% confidence. Hypothesis Testing (For t distribution –two sample) Question 13.4 Random sampling from two normal populations produced the following results: x 1 = 63 x 2 = 60 s1 = 18 s2 = 7 n1 = 50 n2 = 45 a. Estimate with 90% confidence the difference between the two populations means. Hypothesis Testing (For population –two sample) Question 13.70 Random samples from two binomial populations yielded the following statistics: p̂ 1 = 0.45 p̂ 2 = 0.40 n1 = 100 n2 = 100 a. Calculate the p-value of a test to determine whether we can infer that the proportions differ.