Question

The western gull (Larus occidentalis) is a large white-headed bird found along the west coast of North America, from Mexico to BC. The gulls nest in early May, typically laying between 1 and 3 eggs. Suppose that a researcher suspects that the mean weight of the first egg laid of a clutch is different from the mean weight of the second egg. Fourteens eggs are collected from 8 nests, and their weights in grams recorded below. Using this data, perform a hypothesis test to evaluate the researcher's claim. If needed, assume that egg weights are normally distributed. Nest ID 1 2 3 4 5 6 7 8 First Egg (F) 72 90 85 96 112 98 90 98 Second Egg (S) 77 90 81 84 98 88 98 91 (a) (1 mark] Define the parameter(s) of interest using the correct notation. Then, state the null and alternative hypotheses for this study. [1 mark] Calculate the observed value of the test statistic. State the distribution (and degrees of freedom if needed) it follows.

Answer 1

Answer:

Given that:

Nest ID	1	2	3	4	5	6	7	8
First Egg(F)	72	90	85	96	112	98	90	98
Second Egg(S)	77	90	81	84	98	88	98	91

a) Define the parameter of interest using the correct notation.Then,state the null and alternative hypothesis for this study

Here the parameter of interest is mean difference of weight of first and second egg

The null and alternative hypothesis is

$H_0:\mu _d=0\, \, vs\, \, H_1:\mu _d\neq 0$

b) Calculate the observed value of the test statistic.State the distribution (and degrees of freedom if needed) if follows

From the given data $n=8,\bar{d}=4.25,s_d=8.01$

Test statistic $t=\frac{\bar{d}}{\frac{s_d}{\sqrt{n}}}$

$t=\frac{4.25}{\frac{8.01}{\sqrt{8}}}$

$t=\frac{4.25}{\frac{8.01}{2.828}}$

$t=\frac{4.25}{2.8323}$

$t=1.501$

$df=n-1$

$df=8-1$

$df=7$

c) Compute the p-value or provide a range of appropriate values for the p-value

P-value range is 0.1 and 0.2

d) Using the significance level $\alpha$ = 0.05,state your conclusions regarding the difference in egg weights

The P-Value >0.05,So do not reject $H_0$

So,the mean weight of the first egg laid of a cluch is different from the mean weight of the 2nd egg