Question

the wechsler adult intelligence scale (iq test) is constructed so that full scale iq scores follow a normal distribution, with a mean of 100, and a standard deviation of 15. the mayor of smart town believes the countys residents are smarter than the national average and wants to use it (the intelligence of the residents) as a marketing tool to bring industries to the area. a researcher is hired to conduct a study to determine whether smart countys residents have, on average, higher full scale iqs than the population. a random sample of 100 people from smart county were given the iq test and were found to have an average full scale iq of 105. what are the null and alternative hypotheses? a. ( h_0: mu = 105; h_a: mu
eq105 ) b. ( h_0: mu = 105; h_a: mu > 105 ) c. ( h_0: mu = 100; h_a: mu
eq100 ) d. ( h_0: mu = 100; h_a: mu > 100 )

Explanation:

The null hypothesis ($H_0$) is usually a statement of no - effect or equality. Here, the national average IQ is 100. The alternative hypothesis ($H_a$) is what we are trying to find evidence for. The mayor believes the county's residents are smarter than the national average, so we are testing if the mean IQ ($\mu$) of Smart County residents is greater than 100.

Answer:

D. $H_0: \mu = 100; H_a: \mu>100$