Confidence Intervals。。。

kaming0614

2013-05-13 1:30 am

1. A light bulb manufacturer sells a light bulb that has a standard deviation of 33.7 hours. A new manufacturing process is being tested and there is interest in knowing the mean life of the new bulbs. How large a sample is required so that with 95% confidence, the sample mean will deviation from the population mean life by less than 5 hours?

2. In order to estimate the percentage of a large class of statistics students that achieved grade A from a mid-term test, sample of 50 students was taken and 9 students achieved grade A in the mid-term test. Find a 90% confidence interval for the percentage of this statistics class students having grade A in the mid-term test.

回答 (1)

myisland8132

2013-05-13 10:26 pm

✔ 最佳答案

1 σ = 33.7, Z_(α/2) = 1.96

Let Z_(α/2) * (σ/√n) < 5

1.96 * (33.7)/√n < 5

n > 174.5

So, at least 175 light bulbs are need to form the testing

2 p = 9/50 = 0.18, p(1 - p) = 0.1296, √[p(1 - p)/n] = 0.05091

So, the 95% confidence interval is

p - Z_(α/2) √[p(1 - p)/n] < p_0 < p + Z_(α/2) √[p(1 - p)/n]

0.18 - 1.645 * 0.05091 < p_0 < 0.18 + 1.645 * 0.05091

0.09625 < p_0 < 0.2637

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