The mean and standard deviation of a random sample of n measurements are equal to and , respectively. a. Find a % confidence interval for if n. b. Find a % confidence interval for if n. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?

Complete Question

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a

b

c

Generally the width at  n =  49 is mathematically represented as

Generally the width at  n =  196 is mathematically represented as

d

The correct option is E

Step-by-step explanation:

From the question we are told  that

   The sample mean is  

    The standard deviation is  

Generally given that the confidence level is 95% then the level of significance is  

=>    

Generally from the normal distribution table the critical value  of   is  

Considering question a

From the question  n  =  49

Generally the margin of error is mathematically represented as  

=>  

=>  

Generally 95% confidence interval is mathematically represented as  

=>    

Considering question b

From the question  n  =  196

Generally the margin of error is mathematically represented as  

=>  

=>  

Generally 95% confidence interval is mathematically represented as  

=>  

Considering question c

Generally the width at  n =  49 is mathematically represented as

Generally the width at  n =  196 is mathematically represented as

Now when the sample size is quadrupled i.e from n = 49 to  n =  196  

The width of the  confidence interval  decrease by 2 from 1.904 to  0.9374  

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step-by-step explanation:

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