Scenario 1 In a marketing research project, a major supermarket wants to study t

Question

Scenario 1 In a marketing research project, a major supermarket wants to study the relationship between the annual consumption of ramen noodles (Y , in number of packs) and the annual income level of con- sumers (X , in $000s). Based on a random sample of 100 customers, the linear regression model

Yi =?0 +?1Xi +?i
is estimated with the following result:

Coefficient Standard Error Intercept 55.4 32.3 Annual income (in $000s) ?0.22 0.1

Refer to Scenario 1. What is the predicted annual consumption (in number of packs) of ramen noodles for a consumer who earns $100,000 a year?

A) 2.2 B) 22.0 C) 33.4 D) 53.2 E) 55.4

Refer to Scenario 1. To see whether income level has an effect on the consumption of ramen noodles, Adam, Simon and Tim consider the following hypotheses:

H0 : ?1 = 0 Ha : ?1 ?= 0
They arrive at the following conclusions:

Adam: The null hypothesis is rejected at the 5% significance level. Simon: The null hypothesis is rejected at the 2% significance level. Tim: The null hypothesis is rejected at the 1% significance level.

Who is/are correct?

A) Tim only
B) Simon only
C) Adam only
D) Adam and Simon only E) Adam, Simon and Tim

Explanation / Answer

Assuming the intercept coefficient is 55.4 and slope coeff is 0.22, the predicted annual consumption (in number of packs) of ramen noodles for a consumer who earns $100,000 a year is 55.4 + 0.22*100 = 77.4

For hypothesis testing

0.22/0.1 = 2.2

Z-value at 5% two tail =1.96

Z-value at 2% two tail =2.33

Only for 5% the null is rejected as calculated statistic is greater than critical value, hence the null is rejected only at 5% level... Hence (C) only ADAM is correct

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