okay heres the question and the answer I have, but Im not sure its right because the values seem way too high to interpet what it means..:
Data: 63.4,65.0,64.4,63.3,54.8,64.5,60.8,49.1,51.0
"Assume that these observations on SRS from the late Cretaceous atomsphere; (data are % nitrogen from measurements of amber specimens taken from the late Cretaceous era) Do these data give good reason to think that the % of Nitrogen in the air during that time is different from the present 78.1%? Carry out a test of significance at the alpha level of 1%.
My Answer:
Ho:Mu=0 Ha: Mu>0
Xbar=59.59, Sx=6.255, n=9,DF=8 MuX=78.1
T=-8.8776? which gives Table A3 value based on 8 DF=3.355.. this seems off to me... :-(
PLEZ HELP!
To determine whether the data provides evidence that the percentage of nitrogen in the air during the late Cretaceous era is different from the present 78.1%, you need to perform a hypothesis test.
Your answer shows that you have correctly setup the hypotheses. The null hypothesis (Ho) states that the mean percentage of nitrogen during the late Cretaceous era is equal to the present value (78.1%). The alternative hypothesis (Ha) states that the mean percentage of nitrogen is different from the present value.
To perform the hypothesis test, you need to calculate the test statistic and compare it with the critical value at the given alpha level of 1%.
To calculate the test statistic, you need to find the sample mean (Xbar), sample standard deviation (Sx), sample size (n), and the population mean (MuX).
From the data you provided:
- The sample mean (Xbar) is 59.59.
- The sample standard deviation (Sx) is 6.255.
- The sample size (n) is 9.
- The population mean (MuX) is 78.1.
To calculate the test statistic (T), you can use the following formula:
T = (Xbar - MuX) / (Sx / sqrt(n))
Substituting the values we have:
T = (59.59 - 78.1) / (6.255 / sqrt(9))
T = -18.51 / (6.255 / 3)
T = -18.51 / 2.085
T = -8.8776
Your calculation of T = -8.8776 is correct.
Now, you need to compare this test statistic with the critical value from Table A3 for a one-tailed test at the alpha level of 1% and 8 degrees of freedom (DF).
The critical value from Table A3 for one tail at 1% and 8 DF is approximately 2.896.
Since the absolute value of our test statistic (8.8776) is greater than the critical value (2.896), we reject the null hypothesis.
This means that there is evidence to suggest that the percentage of nitrogen in the late Cretaceous atmosphere was different from the present value of 78.1%.
Note: The values you provided for Table A3 seem incorrect because the critical value for a one-tailed test at alpha 1% and 8 DF should be positive (since the alternative hypothesis is in the positive direction). Please double-check the values in your Table A3 for 8 DF.