【四技應用統計學】信賴區間與假設檢定 @ wszspj2的部落格

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【四技應用統計學】信賴區間與假設檢定

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有兩題原文題1.Charter bus records show that in past years, the buses carried an averageof 【42】 people per trip to Niagara Falls. The standard deviation of the population in the past was found to be 【8】. This year, the average of 【10】 trips showed a mean of 【48】 people booked . Can one reject the claim, at α=... 顯示更多有兩題原文題 1.Charter bus records show that in past years, the buses carried an averageof 【42】 people per trip to Niagara Falls. The standard deviation of the population in the past was found to be 【8】. This year, the average of 【10】 trips showed a mean of 【48】 people booked . Can one reject the claim, at α= 【0.10】, that the average is still the same? Find the 【90%】 confidence interval of the mean. Does the confidence interval interpretation agree with the hypothesis-testing results? Explain .Assume that the variable is normally distributed. 2.From past studies the average time college freshen spend studying is 【22】 hours per week. The standard deviation is【 4】 hours . This year, 【60】 students were surveyed, and average time that they spent studying was 【20.8】hours . Test the claim that the time students spend studying has changed. Use α=【 0.01】. It is believed that the standard deviation is unchanged. Find the【 99%】 confidence interval of the mean. Do the results agree? Explain.

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1. Null hypothesis是兩個平均値相同. 90%的信賴區間是(42-1.645*8, 42+1.645*8)=(29, 55),包含樣本平均, null hypothesis is accepted. s.e.=8/√10=2.53, Z=|48-42|/s.e.=2.37 > 1.645, null hypothesis is rejected. 結論與上不同,產生了"Type I error". 2. Null hypothesis是兩個平均値相同. a=0.01的Z值為2.575. 99%的信賴區間是(22-2.575*4, 22+2.575*4)=(11.7, 32.3),包含樣本平均, null hypothesis is accepted. s.e.=4/√60=0.517, Z=|20.8-22|/0.517=2.324 < 2.575, null hypothesis is accepted.

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