Question

Using the 95% CI given on the prior problem (repeated here);

Variable	n	Sample Mean	Std. Err.	L. Limit	U. Limit
pH_level	90	4.577889	not given	4.5181427	4.6376348

What are the upper and lower bounds if we had constructed a 90% confidence interval, using the same sample data?

	a.	(4.518 ; 4.638)
	b.	(4.528 ; 4.628)
	c.	(4.559 ; 5.717)
	d.	(4.507 ; 4.649)
	e.	(4.757 ; 4.899)

Answer 1

95% confidence limit = ( 4.5181427, 4.6376348 )

Sample mean = 4.577889

We need to construct the limit for 90% confidence interval

Now, obtain margin of error

margin of error = Upper limit - mean = 4.6376348 - 4.577889

margin of error = 0.0597458

z_c for 90% CI = 1.645

z_c for 95% CI = 1.96

This is the only difference in margin of error

New margin of error = ( margin of error /1.645)*1.96

New margin of error = (   0.0597458 / 1.645 )*1.96

New margin of error = 0.0711864

95% confidence interval = ( mean - new margin of error , mean + new margin of error )

95% confidence interval = ( 4.577889 - 0.0711864, 4.577889 + 0.0711864 )

95% confidence interval = ( 4.507, 4.649 )