Do one of the following, as appropriate: (a) Find the critical value z_alpha/2,

Question

Do one of the following, as appropriate: (a) Find the critical value z_alpha/2, (b) find the critical value t_alpha/2, (c) state that neither the normal nor the t distribution applies. 98%; n = 7; sigma = 27; population appears to be normally distributed. A) t_alpha/2 = 1.96 B) z_alpha/2 = 2.05 C) z_alpha/2 = 2.33 D) t_alpha/2 = 2.575 Use the given degree of confidence and sample data to construct a confidence interval for the population mean p. Assume that the population has a normal distribution. n = 12, x = 24.9, s = 6.5, 99% confidence A) 19.80

Explanation / Answer

Formula for calculating Confidence Interval= X ± [(z×sd) / n0.5]

where X is mean of the sample

Z represents the appropriate z value from the standard normal distribution for your desired confidence level

sd is standard deviation

n is the sample size.

here 'sd' is 99 , z=1.96 for 95% confidence level .

As the sample mean should be within $2 of population mean,hence

[(z×sd) / n0.5] = 2

or n0.5 = (1.96 * 99)/2

or n=(97.02)2

or n=9412 or 9413(option c)..........answer

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