Question

The sampled population is normally distributed, with the given information. (Give your answers correct to two decimal places.) n = 13, x = 28.8, and σ = 5.6

(a) Find the 0.95 confidence interval for μ.

_________ to ________

(b) Are the assumptions satisfied? Explain.

Yes, the sampled population is normally distributed.

No, the sample distribution is not normally distributed.

not enough information

Answer 1

Solution :

Given that,

a)

Point estimate = sample mean = = 28.8

Population standard deviation =    = 5.6

Sample size = n =13

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z_{0.025 = 1.960}

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

=1.960 * ( 5.6/ 13 )

= 3.044

At 95% confidence interval estimate of the population mean is,

- E < < + E

28.8-3.044 < < 28.8+3.044

25.76 < 31.84

(25.76,31.84)

b) Yes .the sampled population is normally distributed.