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

You’d like to find a range of wingspans that would include 95% of the birds. Find an appropriate average. (Hint: Remember the assumptions for confidence intervals.)

*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

Solution

The range of wingspans that would include 95% of the birds is nothing but the 95% confidence interval for the mean wingspan.

Let X = bird wingspan

Let μ and σ be the mean and standard deviation of X.

100(1 - α) % Confidence Interval for population mean μ, when σ is not known is: Xbar ± MoE........ (1)

where

MoE = (t_{n- 1, α /2})s/√n ....................................................................................................................... (1a)

with

Xbar = sample mean,

t_{n – 1, α /2} = upper (α/2)% point of t-distribution with (n - 1) degrees of freedom,

s = sample standard deviation and

n = sample size.

Calculations

n	30	1-(α/2)	0.975
Xbar	365.4667	n - 1	29
s	63.1963	sqrt(n)	5.4772
α	0.05
tα/2	2.0452
MoE	23.5979
Lower Limit	341.8688
Upper Limit	389.0646

Excel functions:

Xbar – Statistical AVERAGE

s - Statistical STDEV

t_α/2 – Statistical TINV

sqrt(n) - Math & Trig SQRT

Thus, the range of wingspans that would include 95% of the birds is:

[341.9, 389.1] Answer

DONE