Question

In Problems 1 - 3, assume that the population of x values has an approximately normal distribution. Answers may vary slightly due to rounding to TWO decimals:

(a) What is the level of significance? State the null and alternate hypothesis. (b) What sample distribution will use? Write the formula for test statistic and find the value? (c) Find the P-Value of the test statistic. (d) Sketch the graph of sampling distribution and show the area corresponding to P-Value. (e) Based on your answers in parts (a) to (d), will you reject or fail to reject the null hypothesis? (f) Interpret your conclusion in the context of the application.

1. According to a study, the mean cost of bariatric (weight loss) surgery is μ= $21,500. You this this information is correct. You randomly select 25 bariatric surgery patients and find that the mean cost for their surgeries is $20,695. From past studies, the population standard deviation is known σ=$2250 and the population is normally distributed. Is there enough evidence to support your claim at α=0.05? Use p-value.

(15 – Pts)

Answer 1

a) The level of significance is 0.05

We are testing,

H0: u=21500 vs H1: u is not equal 21500

So from H1, we see that we have a two tailed hypothesis test.

b) Since population SD is known, we can use a z distribution here

Test statistic: (Sample mean-21500)/(population SD/√n)

= (20695-21500)/(2250/√25) = -1.79 (rounded to two decimals)

c) p-value of this two sided z test is:

2*P(z<-1.79) = 0.0735 (from the standard normal distribution tables)

d) We will draw a normal curve here.

e) Since the p-value of our test is 0.0735 >significance level of 0.05, we have insufficient evidence to Reject H0 at the 5% level of significance here.

f) Since we fail to Reject H0, we conclude that u=21500