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e A manufacturer claims that the new nickel  metal hydride battery used in mobile phones has a talking time of 300 minutes before recharging. A researcher selected 45 samples with new battery and found that the mean talking time is 294.4 minutes with a standard deviation of 15.03 minutes. Is there enough evidence to conclude that the mean talking time is not 300 minutes as stated at α = 0.01? Find the 99% confidence interval of the true mean. e

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e A report states that the average height of females in the U.S who are in between 18 and 25 years of age are approximately 64.8 inches. The mean of the height of 10 females in the age group of 18 to 25 years is found as 62.4 inches with a standard deviation of 2.5 inches. Can one reject the report at α = 0.05? Find the 95% confidence interval. Does the 95% confidence interval cantain the hypothesized mean? e

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e A nutritionist claims that the number of calories in one table spoon of the major brands of pancake syrup is 180. A sample of 18 major brands of syrup is selected and found that the mean number of calories in one tablespoon of syrup is 156 with a standard deviation of 54. At α = 0.1, can the claim be rejected? Also find the 90% confidence interval of the true mean. e

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e A cigarette manufacturer claims that the nicotine content of its cigarette is 1.05 mg. A sample of 20 cigarettes were selected and found that the mean nicotine content is 1.40 mg with a standard deviation of 0.77 mg. At α = 0.05, is there enough evidence to reject the manufactutrer's claim? Also find 95% confidence interval for the true mean. e

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e A manufacturer claims that the mean content of soft drink in bottles is 300 ml. The contents vary normally with standard deviation σ = 4 ml. A sample of 40 bottles are randomly selected and tested. A 5% significance test rejects H_{0} if z ≤  1.65, where z is the test statistic. Find the power of this test against the alternative μ = 299. e

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e A manufacturer claims that the rods manufactured in their factory have a diameter of 8.5 cm. A random sample of 80 similar iron bars were tested and found that the mean diameter is 8.43 cm and the variance is 0.032 cm^{2}. Is there enough evidence to conclude that the diameter of the iron bars is not 8.5 cm as stated at α = 0.05? Also, find the 95% confidence interval of the true mean. e

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e A cement manufacturer claims that the maximum final setting time of cement is 10 hours. A sample of 13 bags were tested and found that the mean of the maximum final setting time was 11.2 hours with a standard deviation of 1.8 hours. At α = 0.01, can the claim be rejected? Also find the 99% confidence interval of the true mean. e

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e The report of a municipal corporation states that the average monthly electricity bill of a household in the city is $75. To test this report, a researcher selected a sample of 120 residential electricity bills and found the mean as $76.50 with a standard deviation of $15. At α = 0.01. Can the statement be rejected? Also find the 99% confidence interval of the true mean. e

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e A manual of Medical Information reports that the average weight of a new born baby is 7 pounds. As per the data collected from 14 maternity hospitals, the average weight of a newborn was 7.1 pounds with a standard deviation of 0.2 pounds. Is there enough evidence to reject the report at α = 0.05? Also, find the 95% confidence interval of the true mean. e

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e A chocolate manufacturing company reported that milk chocolate bars of 1.5 to 1.6 ounce have 230 calories on an average. A researcher selected a sample of 100 chocolate bars and found the average as 229.6 calories and a standard deviation of 2.3 calories. Is there enough evidence to reject the manufacturer's report at α = 0.1? Also find the 90% confidence interval of the true mean. e

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e A survey report states that the average coffee consumption of the American adult is 400 cups per annum. The annual coffee consumption of 25 American adults was subjected to a study and it was found that the sample has a mean of 418 cups with a standard deviation of 12 cups. At α = 0.10, can the report be rejected? Also find the 90% confidence interval of the true mean. e

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e A magazine report stated that the average business traveler will spend $180 per week on calls. A sample of 20 business travelers are selected at random and their mean expenses was found as $185 with a standard deviation $15. Is there enough evidence to reject the report at α = 0.01. Also, find the 99% confidence interval of the true mean. e

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e An obesity clinic states that the average weight loss after a 15week program of regular aerobic exercise is 8 pounds with a standard deviation of 2.8 pounds. To test this report, a statistician selected 55 people doing regular aerobic exercise and found the average weight loss as 7.4 pounds. Is there enough evidence to reject the claim at α = 0.05? Also find the 95% confidence interval of the true mean. e

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e It is accepted that in the population there is a relationship between the experience and level of income. However, in the sample, the statistical analysis indicates that one cannot reject the null hypothesis at 5% level and thus the null hypothesis is accepted. Identify the type of error made. e

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e A food processing company must decide to accept or reject an entire shipment of potatoes based on the detailed examination of just a small number of potatoes selected at random from the shipment. The catalog states that the mean weight of a bag is 5 pounds with a standard deviation of 0.15. A sample of thirty two 5 pound bags of potatoes are selected at random for testing. A 1% significance test rejects H_{0} if z ≤  2.326, where z is the test statistic. Find the power of this test against the alternative μ = 4.99. e

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e A coin is tossed 100 times. Accept the hypothesis if the number of heads is between 40 and 60. What is the probability of accepting the hypothesis that the coin is fair when the actual probability of heads is 0.6? e

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e Select the incorrect statement(s). I. If a confidence interval does not include H_{0}, then a hypothesis test will reject H_{0}. II. If a confidence interval include H_{0}, then a hypothesis test will reject H_{0} III.For testing H_{0}, t distribution is appropriate when the standard deviation is estimated from the sample data IV. A null hypothesis is most strongly rejected when the Z value is close to zero. e

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e Select the correct statement(s). I. The probability of commiting a type I error is denoted as α II. The probability of commiting a type II error is denoted as β III. A type I error occurs if one rejects the null hypothesis when it is true. IV. The level of significance is the maximum probability of commiting a type II error. e

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e If the blood pressure of healthy men is normally distributed with a mean of 120 mm Hg and a standard deviation of 8, and men with blood pressure levels over 140 mm Hg are diagnosed as not healthy, then what is the probability of a type I error? e

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e In a hypothesis testing, as the probability of committing a type I error increases, then: I. The probability of committing a type II error decreases. II. The probability of committing a type II error increases. III. The power of the test increases. IV. The power of the test decreases. e

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e As the difference between the null hypothesis and the actual assumption increases, then: I. The power of the test increases. II. The probability of committing a type II error decreases. III. The probability of committing a type II error increases. IV. The probability of committing a type I error increases. V. The probability of committing a type I error decreases. VI. The probability of committing a type I error never changes. e

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e Select the correct statement(s). I. If 0.08 significance level is selected in designing a decision rule, then we are 80% confident that we have taken a right decision. II. If 0.01 significance level is selected in designing a decision rule, then we are 90% confident that we have taken a right decision. III. If 0.02 significance level is selected in designing a decision rule, then there are about 2 chances in 100 that would reject the hypothesis when it should be accepted. IV. If 0.05 significance level is selected in designing a decision rule, then there are about 50 chances in 100 that would reject the hypothesis when it should be accepted. e

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e A manufacturer of incandescent bulbs claims that the average life time of a bulb is 1,000 hours with a standard deviation of 1.6 hours. The inspection department selected a random sample of 42 incandescent bulbs and found their average life time as 998.50 hours. At α = 0.1, can the claim be rejected? Also find the 90% confidence interval of the true mean. e

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e It is well known that in the population there is no relationship between the gender and the number of hours they play. But in the sample used, there is a relationship, significant at 5% level. So, the null hypothesis is rejected. Identify the type of error made. e

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e The cholesterol level of healthy men is normally distributed with a mean of 190 mg/dL and a standard deviation of 15. At what level (in excess of 190 mg/dL) should men be diagnosed as not healthy if the probability of a type I error is 2.5%? e

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