Could someone solve this problem step by step?

Question

A tourist agency in California claims the mean daily cost of meals and lodging for family of four traveling in California is more than $268. In an annual survey performed by the consumer protection advocacy you work for, a random sample of 45 families of four traveling in California had a mean daily cost of meals and lodging of $277 with a standard deviation of $40. At α = 0.05, use the information to interpret the claim.

Answer 1

HO : population mean = 268

H1 : population mean > 268

population standard deviation unknown but sample size is large > 30, so use z test

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test statistic = ( 277 - 268) / 40 / √45 = 1.51

Right tailed test as H1 has >

critical value of Z when alpha = 0.05 is 1.64

as 1.51 < 1.64 we have insufficient evidence to reject H0 (and accept H1) so insufficient evidence to support the claim made.

Answer 2

The error is E=40/ sqrt(45)

= 40/ [ 3 * sqrt(5)]

= 40/3*sqrt(5)

= 29.81424

Test stat is

1.96* (268-277)/E

Which is about 0.46

Aaccept Null Hypothesis