Question

7. We take a random sample of 10 eggs and measure their fat content. It is found that for this sample the average fat content is 5.5 g with a standard deviation of 0.4 g. We are interested in determining if the mean fat content of eggs is greater than 5 g.

   1. (a) Define the parameter of interest, and state the hypotheses in terms of the parameter.

   2. (b) State the test statistic you will use. What distribution (including degrees of freedom, if appropriate) you will use to calculate the p-value.

   3. (c) Find the observed value of the test statistic.

   4. (d) Compute (or bracket) the p-value within the accuracy of the tables.

   5. (e) What level of evidence against H0 do you find?

   6. (f) If we were testing our hypothesis at the level α = 0.01, would we reject H0? Explain

      why or why not. In order to receive a mark, you must provide a (correct) explanation.

Answer 1

Solution

Part (a)

Parameter of interest: Mean fat content in eggs, µ Answer   1

Hypotheses in terms of the parameter:

Null H₀: µ = µ₀ = 5   Vs Alternative H_A: µ > 5. Answer 2

Part (b)

Test statistic:

t = (√n)(Xbar - µ₀)/s, Answer 3

where

n = sample size;

Xbar = sample average;

s = sample standard deviation.

Distribution for use to calculate the p-value.

Under H₀, t ~ t_{n – 1} and p-value = P(t > t_{n – 1}) Answer 4

Part (c)

Observed value of the test statistic = 3.9528 Answer 5

Details of Calculations are given at the end.

Part (d)

Using Excel Function, Statistical TDIST,

p-value = 0.00167 Answer 6

Part (e)

Level of evidence against H₀ = 0.99833 [1 – p-value] Answer 7

Part (f)

At the level α = 0.01, we would reject H₀Answer 8

Because p-value (0.00167) < α (0.01) Answer 9

DONE