Question

A toy company wants to know the mean number of new toys per child bought each year. Marketing strategists at the toy company collect data from the parents of 50 randomly selected children. The sample mean is found to be 4.7 toys per child, and the sample standard deviation is calculated to be 1.5 toys per child per year.

Assume that the population standard deviation is unknown. What is the upper bound for a 99% confidence interval? Group of answer choices 5.21 4.35 5.42 5.27

Answer 1

)solution

Given that,

= 4.7

s =1.5

n = 50

Degrees of freedom = df = n - 1 = 50- 1 = 49

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

t   df = t0.01,49 = 2.405 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 2.405* (1.5 / 50) = 0.51

The 99%upper confidence interval mean is,

+ E

4.7 + 0.51

( 5.21)