Question

For a data set obtained from a sample, n = 79 and x = 45.30 . It is known that o = 4.1.

a. What is the point estimate of u?

The point estimate is ????????.

b. Make a 90% confidence interval for u .

Round your answers to two decimal places.

(???????, ??????)

c. What is the margin of error of estimate for part b?

Round your answer to three decimal places.

E =???????

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 45.30

Population standard deviation =    = 4.1

Sample size = n =79

(a) Point estimate =45.30

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2 * ( /n)

= 1.645 * ( 4.1 /  79 )

E= 0.7588
(b)At 90% confidence interval estimate of the population mean
is,

- E < < + E

45.30- 0.7588 <   < 45.30+ 0.7588

44.5412 <   < 46.0588

(44.54 , 46.06 )

(c)Margin of error = E = 0.759