Question

Bird wingspan
479
291
432
314
402
321
479
313
356
413
454
306
349
337
331
317
405
403
356
255
300
362
352
351
518
424
366
315
304
359

A seabird species has a population average wingspan of 403 mm with a variance of 102 mm. You discover a group of birds that look a lot like this seabird on a remote island. You measure wingspan in a sample of 30 individuals from the remote island. You want to know if the birds on the island have a wingspan similar to the well-studied species.

*I will have to solve this using Excel. Specifically what should I do? What functions could I use? For the question, I have to

1. A null and alternative hypothesis stated, as appropriate and for each hypothesis tested. may involve several hypothesis tests.

2. Choose the most appropriate test. Explain how you have met the assumptions of the test or why the test is robust to violations of the assumptions.

3. State explicitly what test(s) you are using.

4. If you fail to reject the null hypothesis, calculate the power of the test.

Answer 1

1.

The Null and Alternative Hypotheses are defined as,

This is a two-tailed test.

Let the significance level = 0.05

2.

The necessary assumptions to perform hypothesis tests are,

1) The samples are randomly and independently selected

2) The populations are approximately normally distributed

3) The population standard deviation is known

Since the sample data points are independently selected, the population standard deviation is known and the sample size is greater or equal to 30, the z test for one population mean is used to test the hypothesis.

3.

The z test for the one population mean is used to test the hypothesis.

4.

The test is performed in excel. The screenshot is shown below,

Conclusion:

Since the P-value is less than the significance level = 0.05 at a 5% significance level, the null hypothesis is rejected.

Alternatively,

The p-value can directly be calculated using the following function in excel