Question

Demand function for Greek yogurt is assumed to be: Q^{GY =} B₀ + B₁ * P^GY + B₂ * P^NGY + E

Q^GY : demand quantity of Greek yogurt. P^GY: price of Greek yogurt. P^NGY: price of Non-Greek yogurt.

(1) What signs do you expect on B₁ and B₂? Why

B₀, B₁, B₂ are estimated as follows:

^B₀ = −20.05 with standard error se_^B0 = 36.97. ^B₁ = −19.50 with standard error se_^B1 = 1.35. ^B₂ = 7.56 with standard se_^B2 = 0.98

sample size = 31, significance level α = 0.05, t_{30, 0.975} = ±2.042, t_{30, 0.95} = ±1.697

(2) Write the demand function for Greek yogurt, with B₀, B₁, B₂ replaced with the estimated numerical values.

(3) Do the following hypothesis test and interpret your result. a) Left-tail test: H₀: B₁ = 0 H₁: B₁ < 0. b) Two-tail test: H₀: B₂ = 0 H₁: B₂ ≠ 0

Answer 1

1)

QGY vs PGY

Negative association

If the demand quantity is larger we can expect larger production and hence lower cost of production and thus lower sales price.

QGY vs PNGY

Positive association

If the prices of non-Geek yogurt rise, people will possibly shift their choice towards Geek-yogurt and thus demand will increase for Geek-yogurt

2)

The demand function is defined as,

The estimate of the slope coefficients are,

The demand function is,

3)

a)

Hypothesis:

This is a one-tailed hypothesis

Let the significance level = 0.05

Test Statistic

The t statistic is obtained using the following formula,

P-value

The p-value is obtained from the t distribution table for t statistic = -14.4444, and degree of freedom = n - 3 = 30 - 3 = 27 for one-tailed test.

Conclusion:

since the p-value is less than 0.05 at a 5% significance level, the null hypothesis is rejected hence we can conclude that the variable PGY is statistically significant in the model.

b)

Hypothesis:

This is a two-tailed hypothesis

Let the significance level = 0.05

Test Statistic

The t statistic is obtained using the following formula,

P-value

The p-value is obtained from the t distribution table for t statistic = 7.7143, and degree of freedom = n - 3 = 30 - 3 = 27 for two-tailed test.

Conclusion:

Since the p-value is less than 0.05 at a 5% significance level, the null hypothesis is rejected hence we can conclude that the variable PNGY is statistically significant in the model.