Dr. Olsen is a population biologist who has been studying white oak trees in the
ID: 3309347 • Letter: D
Question
Dr. Olsen is a population biologist who has been studying white oak trees in the Appalachian mountains of Pennsylvania for many years. Every year of his study, he has collected seeds (acorns) from two populations of White Oaks. For each year he wants to know if there is a difference in the size of the acorns between the two populations. Here is the data for the 2015 Acorn Study - click the link, it will take you to a Google spreadsheet where you will need to copy the correct year's data to your own spreadsheet in order to calculate the following data:
Q1: What is the mean weight of the acorns from the Riverside site? (this should be a positive value to 3 decimal places).
Q2: What is the mean weight of the acorns from the Ridgeline site? (this should be a positive value to 3 decimal places).
Q3: Using the data from the prior questions, what is the standard deviation (s-value) to 3 decimal places for the acorn weights from oaks at the Riverside site?
Q4: Using the data from the previous questions, what is the standard deviation (s-value) to 3 decimal places for the acorn weights from oaks at the Ridgeline site?
Q5: Using the data from the prior questions, what is the s2 value (variance) to 3 decimal places for the acorn weights from oaks at the Riverside site?
Q6: Using the data from the previous questions, what is the s2 value (variance) to 3 decimal places for the acorn weights from oaks at the Ridgeline site?
Q7: Below is the equation for calculating the t-value we are using in this problem set, how many degrees of freedom are there if we were going to calculate the t value from the data set in Q2?
Q8: Using the formula above with the means and standard deviations that you have calculated for the White Oak data set, calculate the t-value to 3 decimal places.
Q9: Using the degrees of freedom that you have calculated from the White Oaks data, use the t-Table below to determine the closest critical value if we want a 95% confidence level and a two-tailed distribution.
Q10: Based on the calculated t-value from the White Oak data and the critical value determined from the t-Table, should you "fail to reject" or "reject" the null hypothesis?
Individual weights of Acorns (g)
White Oaks in Riverside White Oaks in Ridgeline
6.242473111 3.063680188
5.138645131 5.063895861
5.319471636 5.503655711
5.558087252 5.909651653
5.949773985 5.597526006
6.172719798 4.542636126
5.419370289 6.601770745
5.620948508 4.789863377
6.265638847 4.148578774
4.554685428 5.001874952
6.021048445 3.973842293
5.75345687 6.332861198
5.886063845 5.379607287
6.172023973 4.254369152
5.681123656 5.414600113
5.444148041 5.00979176
5.51376486 4.257818532
5.592132613 5.069333579
6.225212137 5.495278908
5.172819429 5.233340924
Explanation / Answer
Using minitab we do this .
Stat >>>> basic Statistics >>>> Descriptive Statistics
Output For White Oaks in Riverside
Descriptive Statistics: White Oaks in Riverside
Variable N* Mean StDev Variance
White Oaks in Riverside 0 5.685 0.447 0.200
Q1: What is the mean weight of the acorns from the Riverside site? (this should be a positive value to 3 decimal places).
>> 5.685
Q3: Using the data from the prior questions, what is the standard deviation (s-value) to 3 decimal places for the acorn weights from oaks at the Riverside site?
>> 0.447
Q5: Using the data from the prior questions, what is the s2 value (variance) to 3 decimal places for the acorn weights from oaks at the Riverside site?
>>> 0.200
Output For White Oaks in Riggeline
Descriptive Statistics: White Oaks in Ridgeline
Variable N* Mean StDev Variance
White Oaks in Ridgeline 0 5.032 0.836 0.699
Q2: What is the mean weight of the acorns from the Ridgeline site? (this should be a positive value to 3 decimal places).
>>>5.032
Q4: Using the data from the previous questions, what is the standard deviation (s-value) to 3 decimal places for the acorn weights from oaks at the Ridgeline site?
>>> 0.836
Q6: Using the data from the previous questions, what is the s2 value (variance) to 3 decimal places for the acorn weights from oaks at the Ridgeline site?
>>> 0.699
Using minitab T-test and Confidence interval
Stat >>>> Basics Statistics >>>>> 2-sample T-test
Two-Sample T-Test and CI
Sample N Mean StDev SE Mean
1 20 5.685 0.447 0.10
2 20 5.032 0.836 0.19
Difference = (1) - (2)
Estimate for difference: 0.653
95% CI for difference: (0.219, 1.087)
T-Test of difference = 0 (vs ): T-Value = 3.08 P-Value = 0.004 DF = 29
Q7: Below is the equation for calculating the t-value we are using in this problem set, how many degrees of freedom are there if we were going to calculate the t value from the data set in Q2?
>>>29
Q8: Using the formula above with the means and standard deviations that you have calculated for the White Oak data set, calculate the t-value to 3 decimal places
t=(X1bar-x2bar)/ Sqrt(s12/n1+s22/n2)
=3.08
Q9: Using the degrees of freedom that you have calculated from the White Oaks data, use the t-Table below to determine the closest critical value if we want a 95% confidence level and a two-tailed distribution
>>>(0.219, 1.087)
Q10: Based on the calculated t-value from the White Oak data and the critical value determined from the t-Table, should you "fail to reject" or "reject" the null hypothesis?
Critical value = 2.045 ( Using T table )
Conclusion - See T-value is Grater than Critical value so Reject the Null hypothsis
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