The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean weight of 3.8 ounces with a sample standard Deviation of 0.5 ounces. At the 0.05 level of significance, perform a hypothesis test to See if the true mean weight is less than 4 ounces. The correct null and alternative hypotheses are A) $\mathrm { H } _ { 0 } : \mu = 4 ; \mathrm { H } _ { \mathrm { A } } : \mu 4$ B) $\mathrm { H } _ { 0 } : \mu = 4 ; \mathrm { H } _ { \mathrm { A } } : \mu 4 ; \mathrm { H } _ { \mathrm { A } } : \mu = 4$ D) $\mathrm { H } _ { 0 } : \mu

Question

The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean weight of 3.8 ounces with a sample standard Deviation of 0.5 ounces. At the 0.05 level of significance, perform a hypothesis test to See if the true mean weight is less than 4 ounces. The correct null and alternative hypotheses are A) $\mathrm { H } _ { 0 } : \mu = 4 ; \mathrm { H } _ { \mathrm { A } } : \mu > 4$ B) $\mathrm { H } _ { 0 } : \mu = 4 ; \mathrm { H } _ { \mathrm { A } } : \mu < 4$ C) $\mathrm { H } _ { 0 } : \mu > 4 ; \mathrm { H } _ { \mathrm { A } } : \mu = 4$ D) $\mathrm { H } _ { 0 } : \mu < 4 ; \mathrm { H } _ { \mathrm { A } } : \mu = 4$ E) $\mathrm { H } _ { 0 } : \mu = 4 ; \mathrm { H } _ { \mathrm { A } } : \mu \neq 4$

Quizplus · Accepted Answer

Since we are testing if the true mean weight is less than 4 ounces, the null hypothesis should be that the true mean is equal to 4 ounces and the alternative hypothesis should be that the true mean is less than 4 ounces. Therefore, the correct null and alternative hypotheses are:

H0: μ = 4
Ha: μ < 4

This corresponds to option B.

The Weights of Soy Patties Sold by Veggie Burgers Delight H0:μ=4;HA:μ>4\mathrm { H } _ { 0 } : \mu = 4 ; \mathrm { H } _ { \mathrm { A } } : \mu > 4H0​:μ=4;HA​:μ>4

The Weights of Soy Patties Sold by Veggie Burgers Delight $\mathrm { H } _ { 0 } : \mu = 4 ; \mathrm { H } _ { \mathrm { A } } : \mu > 4$