can someone help me solve this Find the critical values Chi2-Right and Chi2-Left
ID: 3175977 • Letter: C
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can someone help me solve this
Find the critical values Chi2-Right and Chi2-Left for the confidence level CL = .99 and sample size 13. A magazine includes a report on the prices of home theater systems. The article states that 14 randomly selected home theater systems had a sample standard deviation of $123. Assuming that the sample is taken from a normally distributed population, construct a 95% confidence interval for the population standard deviation. In a random sample of seven aerospace engineers, the mean monthly income was $6824 and the standard deviation was $340. Assume the monthly incomes are normally distributed and use t-distribution to construct a 95% confidence interval for the population mean monthly income for the aerospace engineers. In a survey of 1037 adults from the US age 65 and over, 643 were concerned about getting the flu. Find a point estimate for the population proportion p of those concerned about getting the flu. Construct a 90% confidence interval for the population proportion. Find the minimum sample size needed to estimate the population proportion at the 99% confidence level in order to insure the estimate is accurate within 4% of the population proportion.Explanation / Answer
1. For sample size, n=13, the degrees of freedom, df=n-1=13-1=12. For 99% confidence interval, alpha=0.01, so each end of the X^2 distribution has an area of 0.005. Therefore, critical value for X^2 left tailed is X^2alpha/2=X^20.005=28.2995 (ans) and critical value for X^2 right-tailed is X^21-alpha/2=X^20.995=3.0738 (ans).
2. The 95% c.i for population standard deviation is as follows:
sqrt[(n-1)s^2/X^2alpha/2]<=s<=sqrt[(n-1)s^2/X^21-alpha/2]
For N=14, df=14-1=13, X^2alpha/2=24.7356, X^21-alpha/2=5.0088
sqrt[13*123^2/24.7356]<=s<=sqrt[13*123^2/5.0088]
89.1693<=s<=198.1572 (ans)
3. The 95% c.i for population mean is as follows:
xbar+-talpha/2, df=N-1 (s/sqrt N), where, xbar is sample mean, t denotes t critical at alpha/2, and df=N-1, s is sample standard deviation, and N is sample size.
=6824+-2.4469(340/sqrt 7)
=6509.55, 7138.45 (ans)
4. The point estimate of population proportion, p is sample proportion, phat=643/1037=0.62 (ans)
The 90% c.i for population proportion is as follows:
phat+-zalpha/2 sqrt[phat(1-phat)/N], where, phat is sample proportion, N is sample size.
=0.62+-1.28 sqrt[0.62(1-0.62)/1037]
=0.60, 0.64 (ans)
Sample size, n=phatg(1-phatg)[zalpha/2/E]^2, where, phatg is proportion of educated guess, z denote z critical at alpha/2, ad E is margin of error.
=0.62(1-0.62)[2.576/0.04]^2
=977.11~977 (ans)
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