a. Estimate, with 95 percent confidence, the mean height for all students enrolled in BMGT 230, lastsemester. b. How would the width of the interval in Part a change if the standard deviation equaled 3.33 inches, holding all other values/ideas constant?c. How would the width of the interval in Part a change if the mean equaled 71 inches, holding all other values/ideas constant?

Complete Question

The complete question is shown on the first uploaded image

a

The 95% confidence interval  is      

b

The width will reduce by one

c

The width will remain the same

Step-by-step explanation:

Considering question a

From the question we are told that

  The sample size is  n = 36

   The standard deviation is  

  The mean is  

From the question we are told the confidence level is  95% , hence the level of significance is    

=>  

Generally from the normal distribution table the critical value  of   is  

Generally the margin of error is mathematically represented as  

=>

=>

Generally the width of the confidence interval is

=>    

=>   =>  

Generally 95% confidence interval is mathematically represented as  

=>    

=>        

Considering question b

when

Generally the margin of error is mathematically represented as  

=>

=>

Generally the width of the confidence interval is

=>    

=>    

So comparing we see that the width will decrease by 1

Considering question b

When  

Generally 95% confidence interval is mathematically represented as  

=>    

Generally the width is mathematically represented as

=>  

Comparing we see that the width of the confidence interval remain the same