Question

To try to determine whether the composition of the earth’s atmosphere has changed over time, scientists can examine the gas in bubbles trapped inside ancient amber.  (That’s the plot of Jurassic Park.) Assume that the following 9 measures are a random sample from the late Cretaceous era (75 to 95 million years ago). The data represent the percent of nitrogen in each sample.

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 the mean is less than 61.

1. Conduct a hypothesis test using a 95% confidence interval.

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 and why.

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 and t-value at which you will reject the null hypothesis. Clearly label the reject and do not reject region.

c. Calculate the test statistic using: x̅ -  μ) / SE where SE =  . s= sample standard deviation.

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

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

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

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

                

            

Answer 1

1)

a) T critical value =  2.306

b) Sample Mean:

c) Sample SD:

d. Standard error = SD / sqrt(n) = 6.2553 / sqrt(9) = 2.0851

e. Calculate the confidence interval.

Lower Limit: Mean - t value 8 SE = 59.5889 - 2.306*2.0851 = 54.781

Lower Limit: Mean +  t value 8 SE = 59.5889 + 2.306*2.0851 = 64.3971

f) We can not conclude that  the population mean is less than 61.

2) a) alpha = 0.05

b) The red color shaded is rejected region

d) Test statistic t = ( x̅ -  μ) / SE

= (59.5889 - 61) / 2.0851 = -1.15635

e. Conclusion: Since t value > t critical value so we accept H0

Thus we conclude that population mean is not less than 61

f. P-value = 0.1404 which is > alpha 0.05 we accept H0

g. Thus we conclude that population mean is not less than 61