Question

In: Statistics and Probability

A toy manufacturer wants to know how many new toys children buy each year. A sample...

A toy manufacturer wants to know how many new toys children buy each year. A sample of 499 children was taken to study their purchasing habits. Construct the 90% confidence interval for the mean number of toys purchased each year if the sample mean was found to be 5.6. Assume that the population standard deviation is 1.9.

Solutions

Expert Solution

Solution :

Given that,

= 62.5

= 8.8

n = 499

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * (1.9/ 499 )

= 0.14

At 90% confidence interval estimate of the population mean is,

- E < < + E

5.6 - 0.14 < < 5.6 + 0.14

5.46 < < 5.74

(5.46 ,5.74)


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