Question

            A local resort claims that the average family spends less than $1,200 on a weekend stay at its facility. A magazine that reviews vacation destinations investigated this result by taking a a random sample of 19 families that have stayed at the resort in the last year. The sample produced a mean of $1224.939 and a standard deviation of $62.69. For the hypotheses:

            H₀: µ = $1,200    and   H_A: µ > $1,200, what is the p-value of the test statistic for this sample?

With explanation of work

Answer 1

Hypothesis : Vs  

Since , the population standard deviation is not known.

Therefore , use t-distribution.

Now , df=degrees of freedom=n-1=19-1=18

The value of test statistic is ,

The p-value is ,

p-value= ; The Excel function is , =TDIST(1.734,18,1)

Decision : Here , p-value =0.05

Therefore , reject Ho.

Conclusion : There is sufficient evidence to support the claim that average family spends less than $1220 on a weeked stay at its facility.