Question

You are maintaining a collection for fwooper , and are trying to adjust their diet to keep them from gaining or losing too much weight. You know that fwoopers in the wild have a mean mass of 125 grams but other than that you don’t know much else.

The data you collect initially about the fwooper mass is in the excel data table.

fwooper mass (g)

1 143.9

2 141.9

3 122.9

4 106.8

5 120.3

6 163.3

7 126

8 111.7

9 111.1

10 111.8

11 131.5

12 122.2

13 99.1

14 127.4

15 116.4

16 113.6

17 144

18 111.8

19 117.1

20 108.1

21 149.9

22 108.8

23 156.9

24 103.4

1. Are you comparing two sets, one set of data to a known value?

2. If you are comparing one set of data to a known value, do you know the population variance?

3. If you are comparing two sets of data, are they INDEPENDENT or PAIRED?

4. IF the data are independent do you need to do an F-Test?

5. IF you need to do an F-test, record the results here:( if not put N/A and delete)

• F-test Null Hypothesis: -F-test Alternative Hypothesis:

• F-test ratio(calc): - F-test Critical Value:

6. Which type of hypothesis test are you going to do?

One sample Z test one sample t-test homoscedastic t-test

Heteroscededatic t-test paired t-test

7. For your hypothesis test, record the following:

           Null hypothesis: Alternative Hypothesis: test statistic:

           P-value: df= critical value:      

8. Statistical conclusion: Reject null hypothesis or Fail to reject Null hypothesis

9. Biological Conclusion:

Answer 1

Answer: We are comparing one set of data to a known population mean weight.

Explanation: The is only one set of data is given such that the weight of fwooper, and the known value of population parameter such that the mean weight of the fwooper.

Answer: The population variance is not known

Explanation: For the population, only mean value is given, the population variance of the weight is not known.

Answer: N/A,

Explanation: The F-test is used to test whether the two population variances are equal. Since there is only one set of data is given, we do not need to do an F-test.

Answer: one-sample t-test

Explanation: Since we are comparing one sample mean with the population mean and the population variance is not known, the one-sample t-test is used to test the hypothesis.

Hypothesis test

Null hypothesis: The null hypothesis is defined as the sample weight of fwooper is equal to the population mean weight of fwoopers, i.e.

Alternative Hypothesis: The alternative hypothesis tests the claim that the sample weight of fwooper is not equal to the population mean weight of fwoopers i.e.

test statistic:

The t-statistic is obtained using the following formula,

The t statistic is obtained using the formula,

For calculation purposes, the mean and standard deviation are obtained in excel using the function =Average() and =STDEV(). The screenshot is shown below,

From the data values,

P-value: 0.3653

Explanation: The P-value is obtained from the t distribution table for degree of freedom = n - 1 = 24 - 1 = 23

df = 23

Explanation:

df= n - 1 = 24 - 1 = 23

Critical value:

0.0634, 2.0687

Explanation: The critical value is obtained from the t critical value table for significance level = 0.05 for the degree of freedom = 23 for a two-tailed hypothesis,

t critical (lower) = 0.0634

t critical (upper) = 2.0687

Statistical conclusion:

Fail to reject the Null hypothesis

Explanation: Since the p-value is greater than 0.05 at a 5% significance level, the null hypothesis is rejected

Biological Conclusion: Since the null hypothesis is rejected we can not conclude that the mean of the fwooper is different than 125 grams.