1. Find the value of a/2 shown in the figure below 98%- a. 0.01 b. 0.02 c. 0.04
ID: 3318077 • Letter: 1
Question
1. Find the value of a/2 shown in the figure below 98%- a. 0.01 b. 0.02 c. 0.04 d. 0.05 Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The mean tear wear was found to be 50,000 miles with a standard deviation of 3,500 miles. What is the best estimate of the mean tread life in miles for the entire population? a. 3,500 b. 50,000 2. c. (50,000/100) d. (3,500/100) Ten randomly selected people were asked how long they slept at night. The mean time was 7.1 hours, and the sample standard deviation was 0.78 hours. Find the 95% confidence interval of the mean time 3. they slept at night. 6.65Explanation / Answer
1. Confidence internal = 98% => Alpha value = 0.02 (Answer: B)
2. (Answer: B) 50,000. The population mean is generally in the interval (with 95% confidence):-
( sample_mean - 2*[sample_std_deviation/sqrt(n)], sample_mean + 2*[sample_std_deviation/sqrt(n)] ); n: sample size
=> (49300,50700) => Answer: b) 50,000
3. The 95% confidence interval of population mean from sample mean is defined as follows:-
( sample_mean - 2*[sample_std_deviation/sqrt(n)], sample_mean + 2*[sample_std_deviation/sqrt(n)] ); n: sample size
=> Pop_mean 95% CI = ( 7.1 - 2*0.78/sqrt(10), 7.1 + 2*0.78/sqrt(10) )
= (6.60668,7.5933) [Answer = b] (closest)
4. (Answer: A) When the population standard deviation is unknown
5. (Answer: C) Sample size = 50, CI level = 98%, Degree of freedom = n-1 = 49
=> t(alpha/2) = between 2.39 and 2.423 => Use Excel function "T.INV" to get 2.405 (approx)
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