Question

ULUILLOU Progress Check *14.1 Identifying the treatment group with 4, specify both the and alternative hypotheses for each of the following studies. Select a directional altern hypothesis only when a word or phrase justifies an exclusive concerns about population differences in a particular direction. (a) After randomly assigning migrant children to two groups, a school psychologist deter- mines whether there is a difference in the mean reading scores between groups exposed to either a special bilingual or a traditional reading program. (b) On further reflection, the school psychologist decides that, because of the extra expense of the special bilingual program, the null hypothesis should be rejected only if there is evi- dence that reading scores are improved, on average, for the group exposed to the special bilingual program. (c) An investigator wishes to determine whether, on average, cigarette consumption is reduce for smokers who chew caffeine gum. Smokers in attendance at an antismoking worksho are randomly assigned to two groups one that chews caffeine gum and one tna not-and their daily cigarette consumption is monitored for six months after the wolnom (d) A political scientist determines whether males and females differ, on average amount of money that, in their opinion, should be spent by the U.S. government land security. After being informed about the size of the current budget for nom rity, in billions of dollars, randomly selected males and females are askeu percent by which they would alter this amount-for example, -8 percent i reduction, 0 percent for no change, 4 percent for a 4 percent increase. Answers on page 437. on average, about the government on home- aget for homeland secu- es are asked to indicate the percent for an 8 percent

Answer 1

(a) Here, the psychologist wishes to compare the mean reading scores of two independent groups of students under special bilingual and traditional reading program. Let $\mu _{1},\mu _{2}$ denote the mean reading scores of students under special bilingual and traditional reading program respectively.

The claim to be tested here, is that there is a difference in mean reading scores between groups exposed either to a special bilingual program or a traditional reading program ($\mu _{1}\neq\mu _{2}$).

The claim to be testes is considered the alternate hypothesis and the negation of this claim is taken to be the null hypothesis.

To test:$H_{0}:\mu _{1}=\mu _{2}$ Vs   $H_{a}:\mu _{1}\neq\mu _{2}$

In words,

H0: There is no difference in mean reading scores between groups exposed either to a special bilingual program or a traditional reading program

Ha: There is a significant difference in mean reading scores between groups exposed either to a special bilingual program or a traditional reading program

(b) Here, the psychologist claims that students exposed to the special bilingual program shows improved reading scores as compared to the traditional reading program.

To test:$H_{0}:\mu _{1}\leq \mu _{2}$ Vs   $H_{a}:\mu _{1}>\mu _{2}$

H0: There is no difference in mean reading scores between groups exposed either to a special bilingual program or a traditional reading program

Ha: The students exposed to a special bilingual program have higher mean reading scores as compared to those exposed to a traditional reading program.

(c) Here, we are comparing the difference in daily cigarette consumption of smokers after six months, between those who chew caffeine gum and those who do not. Let $\mu _{d1},\mu _{d2}$ denote the mean difference (Pre - Post six months) in daily cigarette consumption of those who chew caffeine gum and those who do not respectively.

The researcher claims that Chewing caffeine reduces the cigarette consumption.Hence, he would expect a greater reduction in the cigarette consumption levels of those whio chew caffeine during the six month period, i.e. $\mu _{d1}>\mu _{d2}$

To test: $H_{0}:\mu _{d1}\leq \mu _{d2}$ Vs   $H_{a}:\mu _{d1}>\mu _{d2}$

H0: There is no difference in the mean difference in daily cigarette consumption of those who chew caffeine gum and those who do not.

Ha:  The mean difference in daily cigarette consumption of those who chew caffeine gum is greater than those who do not.

(d) Here, we are comparing two independent groups males and females based on their opinion about the amount of money that should be spent by the US government on homeland security. Let $\mu _{1},\mu _{2}$ denote the average percentage of the amount of money that should be spent by the US government on homeland security, according to Males and Females respectively.

The researcher wishes to know whether the two groups differ in terms of the average money to be spent.

To test:$H_{0}:\mu _{1}=\mu _{2}$ Vs   $H_{a}:\mu _{1}\neq\mu _{2}$

H0: There is no difference in average percentage of the amount of money opined to be spent by the US government on homeland security, according to Males and Females

Ha: There is a significant difference in average percentage of the amount of money opined to be spent by the US government on homeland security, according to Males and Females