To try to determine whether the composition of the earth’satmosphere has changed over time, scientists can examine the gas inbubbles trapped inside ancient amber.  (That’s the plotof Jurassic Park.) Assume that the following 9 measures are arandom sample from the late Cretaceous era (75 to 95 million yearsago). The data represent the percent of nitrogen in eachsample.

63.4     65.0     64.4     63.3     54.8     64.5     60.8     49.1     51.0

You asked to conduct a hypothesis test to determine whether themean is less than 61.

1. Conduct a hypothesis test using a 95% confidenceinterval.

a. What value for t will you use?

b. What is the sample mean?

c. What is the sample standard deviation?

d. What is the standard error?

e. Calculate the confidence interval.

f. What conclusion will you draw about the null hypothesis andwhy.

2. Conduct a hypothesis test using the traditional method.

a. Choose a level of significance (a)

b. Draw a t-diagram in which you place the mean at zero andt-value at which you will reject the null hypothesis. Clearly labelthe reject and do not reject region.

c. Calculate the test statistic using: x? -  ?) / SEwhere SE =  . s= sample standard deviation.

d. Place the value you get for t on your diagram. Does it fallin the reject or do not reject region?

e. What is your conclusion? State it in words in the context ofthis problem.

f. Calculate the p-value. Compare the p-value to . Whatconclusion will you draw and why?

g. Your conclusion in e and f should be the same. If not lookover your work.