The Central Limit Theorem states that the distribution of the sample mean ( X ) will be approximately ____________ provided the sample size is ___________.(*) a. normal, large
In the time series decomposition procedure using monthly data, the trend line is determined by finding the "best" line through the _____________ data which are determined by _______ (*) c. deseasonalized, dividing
Mean: average/number of samples
Median: even (two numbers/2) odd(middle number)
Standard deviation: mean (number-mean)(square root); add/divide z-score: (x - μ) / σ
How many of the sample values actually are between x - 2s and x + 2s? (*) e. all of them 3 all of them are between 18.64 and 48.36
The first quartile (average eof the 3rd and 4th ordered Values)
Are the events “Brand A” and “Unmarried Females” independent? (*) e. No, since P(Brand A | Unmarried Females) is unequal to P(Brand A) NOTE: P(Brand A | Unmarried Females) = 35/46 and P(Brand A) = 120/200
What is the probability that the sample contains exactly six 2-door car purchasers? (*)d..207 3useTableA.1withn=15andp=.4tofindP(6)
What is the probability that X is at least 8? (*) e..213 3useTableA.2tofindP(X$8)=1-P(X#7)=1-.787
What is the mean of X? (*) e. 6.0 3 this is np = (15)(.4)
Find P(-1.5 < Z < 2.0) (*) b. .9104
Find the value of Z (say, z) so that P(Z $ z) is 0.65. (*) b. -0.39 3 z must be negative since the area to right of z is more than .5
Find the value of Z (say, z) so that P(-z < Z < z) is 0.82. (*) c. 1.34 3 P(-1.34 < Z < 1.34) is approximately .82
The attendance at concerts given at the Riverside Auditorium is believed to be normally distributed with a mean of 8,500 and a standard deviation of 2,500. Let X represent the attendance at one of the Riverside concerts.
What is the probability that X is less than or equal to 7,000? (*) a. .2743 3 this is P(Z # -.6)
What is the probability that the attendance exceeds 11,000? (*)a..1587 3thisisP(Z>1)
What is the probability that the average attendance for the past 25 concerts at Riverside is more than 9300? (*) c. .0548 3 this is P[Z > (9300 - 8500)/(2500/sqrt(25))] = P(Z > 1.6)
A congressional committee wishes to estimate the average annual subsidy received by tenant farmers in a southern state. A random sample of 19 farms is taken, the sample mean is found to be $6,300 with a standard deviation of $400. What is the upper limit of the 95% confidence interval for the mean annual subsidy? (*) e. $6,493 3 6300 + (2.101)(400)/sqrt(19) NOTE: Use the t table here since $400 is the sample standard deviation.
What sample size would be necessary to estimate the mean annual subsidy to within ± $50 with 95% confidence? (*) d. 246 3 n = [(1.96)(400)/50]2 and round up (always)
In the manufacturing of a certain machine part, the lead content is an important quantity. For each production day, the lead content of five parts is measured. The table below consists of the average of the five lead contents (in mg) for ten consecutive production days. The sum of the 10 sample ranges is 37 and the sum of the 10 sample means (below) is 338.8. Also, the smallest range is 1 and the largest range is 5.
The estimate of the process standard deviation (σ) is *) nd e. 1.591 3 NOTE: the sample size is 5 (see the 2nd line) and not 10 and = 3.7/2.326
The upper control limit for the X chart is (*) c. 36.01 3 33.88 + (3)(1.591)/sqrt(5) = 33.88 + 2.13. NOTE: LCL = 31.75
The upper control limit for the R-chart is (*) a. 7.82 3 (3.7)(2.114)
How many of the ten samples indicate an out of control condition using either the X chart or the R chart? *) b. one 3 sample 10 mean is > 36.01. All ranges < 7.82 since the largest range is 5.
A firm that produces fabric inspects square yards of material for loose threads. The following data represent the number of loose threads found on each of 20 samples inspected (one square yard of material…