Question

Using the p-value approach and α-0.01, test the claim that price of cauliflower has no influence on the demand for tomatoes. U.S. CONSUMPTION OF OR DEMAND FOR TOMATOES FROM 1 SUMMARY OUTPUT Regression Statistics 0.9795 Multiple R Square Adjusted R Square Standard Error Observations 0.9594 0.9552 0.423 ANOVA df Regression Residual 41.314 230.80 1.40982E-26 165.257262 6.983256214 39 0.179 Total 43 172.2405182 Coeficients Standard Error P-value t Stat 0.3750 0.0340 22482 0.0302 0.0143 Intercept Ptomato Pcucumbers Pcauliflower ncome 0.8431 -0.0871 -0.1507 0.0825 0.2537 0.0294 5.1251 8.43254E-06 0.0250 0.0021 0.0186 13.6099 2.13871E-16 Variables Arithmetic Mean for Dependent and I Otomato Ptomato Pcucumbers Peauliflower Income S/cwt S/cwt $1,000 undredweigh)tSet263191 Pounds S/cwt 26.31 14.98 | Mean 3.598

Answer 1

The demand for tomatoes is the dependent variable while the price of cauliflower is the explanatory variable.

If we say that the null hypothesis is that the price of cauliflower has no influence on demand for tomatoes. The alternative hypothesis would thus be that the price of cauliflower is affecting the demand for tomatoes.

As per the p-value criteria, if the p-value of a coefficient is less than the significant level, we reject the null hypothesis while the alternative hypothesis is accepted.

Here, the p-value of the price of cauliflower is 0.0021 which is less than 0.01 (as given in the question) which implies that the null hypothesis can be rejected and thus we accept the alternative hypothesis.

So, the claim that the price of cauliflower has no influence on the price of tomatoes is false as indicated by the rejection of the null hypothesis.