Question

Each of the following statements corresponds (somewhat naturally) to a statistical hypothesis. For each statement, decide

If it involves one or more populations; one or more variables. [No answer needed.]

The population(s) and the variable(s) involved.

The form of the test.

Single parameter

Two parameter or multiple parameter—always the same parameter for multiple populations (or possibly multiple variables)

Single distribution

Two distributions or multiple distributions—either two different variables, or the same variable for multiple populations

Independence

Note with measures of association will have one parameter (g, r, b) with a pair of populations

If the hypothesis is on one or more parameters, give

The parameter(s) involved.

The Null and the Alternate hypotheses. or

Whether the hypothesis test is one or two-sided. or

If the hypothesis is on one or more distributions, give

The Null and the Alternate hypotheses.

Why don’t we need to specify whether one-sided or two-sided?

1.The typical American teenage girl uses her cell phone 27 hours per week.

2.There is a negative association between the severity of a patient’s illness and his/her opinion of food in the hospital.

3.The average Toro Loco bill for a dinner for four is $97.53.

4.The percentage of couples who divorce is higher for those who lived together before marriage than for those who didn’t.

5.70% of all students who need more than three remedial courses in college will not graduate.

Answer 1

1.

a)If the random variable X be defined as X=no. of hours a teenage american girl spends on her mobile phone, then this hypothesis is a one population testing problem i.e., it involves a single variable X.

b)The population would be the population of teenage american girls and the variable involved would be the random variable,  X=no. of hours a teenage american girl spends on her mobile phone.

c)If we make the assumption that X follows univariate normal distribution, then if we know about the sample standard deviation then we'll use the one sample Z-test or else we'll use one sample t-test.

d)Since we are using the assumption that iid ,we ahve 2 parameters but we'll be just be testing for a single parameter .

e)We are considering iid samples.

f) the null hypothesis is

g) The test used will be a 2 sided test because of the above defined null hypothesis.

2.

a)Since this hypothesis involves the measure of the association of the severity of a patient’s illness and his/her opinion of food in the hospital we will use 2 random variables X and Y defined as

X=The degree of severity of a patient's illness

Y=Their opinion on hospital food

b)The variables being categorical variables we'll use a test of association

c) We do not use individual parametric distributions for the variables nut rather use a given contingency table for this

d)The null hypothesis is :

Ho: the degree of severity of a patient's illness is not associated to their opinion on hospital food

H1: the degree of severity of a patient's illness is associated to their opinion on hospital food

e)The test is involves the usage of p-values to reject or accept the null hypothesis.

3.

a)For this we'll use 4 variables X1,X2,X3,X4 where,

Xi=Toro Loco bill for an individual (i=1(1)4)

b)For this test we can assume a Normal distribution with 4 different means and common variances for the 4 respective variables

c) We'll consider the ANOVA for F-test for testing this hypothesis

d)We have 4 different populations having respective univariate normal distributions with varying means and common variance

e)The hypothesis is:

97.53

against

H1: one pair is unequal

f)This is a two sided test

4.

a)We can consider the test as a paired t-test between 2 populations

b)We can consider 2 variables X and Y such that

X= % of divorce among couples who live together

Y = % of divorce among couples who do not live together

c)The hypothesis would be:

Ho: Mean of x=mean of y

H1:mean of x!=mean of y

d)It is a 2 sided test