Suppose you want to test H0: m £ 100 against H1: m > 100 using a significance level of 0.05. The population is normally distributed with a standard deviation of 75. A random sample size of n = 40 will be used. If m = 130, what is the probability of correctly rejecting a false null hypothesis? What is the probability that the test will incorrectly fail to reject a false null hypothesis? In a study of attitudes and job satisfaction, a sample of 50 men and 50 women were asked to rate their overall job satisfaction on a 1 to 10 scale. A high rating indicates higher degree of job satisfaction and the ratings are assumed to be normal with equal standard deviations. The sample of men recorded a mean rating of 7.2 with a standard deviation of 1.7, and the sample of women recorded a mean rating of 6.4 with a standard deviation of 1.4. Do men generally have better job satisfaction than women? Two machines are supposed to be producing steel bars of approximately the same length. A sample of 35 bars from one machine has an average length of 37.013 inches, with a standard deviation of 0.095 inches. For 38 bars produced by the other machine, the corresponding figures are 36.074 inches and 0.032 inches. Using a 0.05 level of significance and assuming equal population standard deviations, can we conclude that the machines are not different from each other? Construct and interpret the 95 percent confidence interval for the difference between the population means. Suspecting that television repair shops tend to charge women more than they do men, Emily disconnected the speaker wire on her portable television and took it to a sample of 12 shops. She was given repair estimates that averaged $95 with a standard deviation of $28. Her friend John was taking the same set to another sample of 9 shops, was provided with an average estimate of $65, with a standard deviation of $21. Using normal populations with equal standard deviations, use a 0.05 significance level in evaluating Emily’s suspicion. What is the approximate p-value of the test?

Suppose you want to test H0: m £ 100 against H1: m > 100 using a significance level of 0.05. The population is normally distributed with a standard deviation of 75. A random sample size of n = 40 will be used. If m = 130, what is the probability of correctly rejecting a false null hypothesis? What is the probability that the test will incorrectly fail to reject a false null hypothesis? In a study of attitudes and job satisfaction, a sample of 50 men and 50 women were asked to rate their overall job satisfaction on a 1 to 10 scale. A high rating indicates higher degree of job satisfaction and the ratings are assumed to be normal with equal standard deviations. The sample of men recorded a mean rating of 7.2 with a standard deviation of 1.7, and the sample of women recorded a mean rating of 6.4 with a standard deviation of 1.4. Do men generally have better job satisfaction than women? Two machines are supposed to be producing steel bars of approximately the same length. A sample of 35 bars from one machine has an average length of 37.013 inches, with a standard deviation of 0.095 inches. For 38 bars produced by the other machine, the corresponding figures are 36.074 inches and 0.032 inches. Using a 0.05 level of significance and assuming equal population standard deviations, can we conclude that the machines are not different from each other? Construct and interpret the 95 percent confidence interval for the difference between the population means. Suspecting that television repair shops tend to charge women more than they do men, Emily disconnected the speaker wire on her portable television and took it to a sample of 12 shops. She was given repair estimates that averaged $95 with a standard deviation of $28. Her friend John was taking the same set to another sample of 9 shops, was provided with an average estimate of $65, with a standard deviation of $21. Using normal populations with equal standard deviations, use a 0.05 significance level in evaluating Emily’s suspicion. What is the approximate p-value of the test?

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Author:Amos Gilat

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Suppose you want to test H₀: m £ 100 against H₁: m > 100 using a significance level of 0.05. The population is normally distributed with a standard deviation of 75. A random sample size of n = 40 will be used. If m = 130, what is the probability of correctly rejecting a false null hypothesis? What is the probability that the test will incorrectly fail to reject a false null hypothesis?
In a study of attitudes and job satisfaction, a sample of 50 men and 50 women were asked to rate their overall job satisfaction on a 1 to 10 scale. A high rating indicates higher degree of job satisfaction and the ratings are assumed to be normal with equal standard deviations. The sample of men recorded a mean rating of 7.2 with a standard deviation of 1.7, and the sample of women recorded a mean rating of 6.4 with a standard deviation of 1.4. Do men generally have better job satisfaction than women?
Two machines are supposed to be producing steel bars of approximately the same length. A sample of 35 bars from one machine has an average length of 37.013 inches, with a standard deviation of 0.095 inches. For 38 bars produced by the other machine, the corresponding figures are 36.074 inches and 0.032 inches. Using a 0.05 level of significance and assuming equal population standard deviations, can we conclude that the machines are not different from each other? Construct and interpret the 95 percent confidence interval for the difference between the population means.
Suspecting that television repair shops tend to charge women more than they do men, Emily disconnected the speaker wire on her portable television and took it to a sample of 12 shops. She was given repair estimates that averaged $95 with a standard deviation of $28. Her friend John was taking the same set to another sample of 9 shops, was provided with an average estimate of $65, with a standard deviation of $21. Using normal populations with equal standard deviations, use a 0.05 significance level in evaluating Emily’s suspicion. What is the approximate p-value of the test?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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