probability and statistic
Joss_Smitx01
Assignment5.docx7.9 Suppose that we will take a random sample of size n from a population having mean m and standard deviation s. For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean x:
a μ=10, σ=2, n=25 c μ=3, σ.1, n=4
b μ=500, σ.5, n=100 d μ=100, σ 1, n=1,600
Again, consider the survey of 350 Bank of America customers discussed in Exercise 7.31, and assume that 48% of Bank of America customers would currently express customer delight. That is, assume p=.48. Find:
a The probability that the sample proportion obtained from the sample of 350 Bank of America customers would be within three percentage points of the population proportion. That is, find P(.45 ≤ pˆ ≤.51).
b The probability that the sample proportion obtained from the sample of 350 Bank of America customers would be within six percentage points of the population proportion.
That is, find P(.42 ≤ pˆ ≤ .54)
8.6 Suppose that, for a sample of size n 100 measurements, we find that x 50. Assuming that s equals 2, calculate confidence intervals for the population mean m with the following confidence levels:
a 95% b 99% c 97% d 80% e 99.73% f 92%
8.16 Suppose that for a sample of n 11 measurements, we find that x 72 and s 5. Assuming normality, compute confidence intervals for the population mean m with the following levels of confidence: a 95% b 99% c 80% d 90% e 98% f 99.8%
8.37 In each of the following cases, compute 95 percent, 98 percent, and 99 percent confidence intervals for the population proportion p.
a pˆ=.4 and n=100
c pˆ=.9 and n=100
b pˆ=.1 and n=300
d pˆ=.6 and n=50
