Question

Freshmen Politics. The Higher Education Research Institute of the University of California, Los Angeles, publishes information on the characteristics of incoming college freshmen in The American Freshman. Incoming freshmen characterized their political views as liberal, as moderate, and as conservative, For this year, a random sample of 500 incoming college freshmen yielded the following frequency distribution for political views. Freshmen Politics. The Higher Education Research Institute of the University of California, Los Angeles, publishes information on the characteristics of incoming college freshmen in The American Freshman. Incoming freshmen characterized their political views as liberal, as moderate, and as conservative, For this year, a random sample of 500 incoming college freshmen yielded the following frequency distribution for political views.

Political view	Frequency
Liberal	147
Moderate	237
Conservative	116

a. Identify the population and variable under consideration here.

b. At the 55 significance level, do the data provide sufficient evidence to conclude that this year's distribution of political views for incoming college freshmen has changed from the 2000 distribution?

c. Repeat part (b), using a significance level of.

Short answer

Ans:

(a) A variable is an attribute or attribute that can be measured. The amount of flexibility may vary for each unit. That is, the variable is defined as the element recorded in each case.

From the given definition, the variables under the study "Political Perspective" because the outcome of each effort can be measured and this number may vary from effort to individual.

(b) According to the output, the value of the test statistic is $4.39410$and the p-value is $0.111$.

(c) Conclusion for significance level:

the data do not provide sufficient evidence to conclude that this year's distribution of political views for incoming college freshmen has changed from the 2000 distribution at a $10\%$level of significance.

Step-by-step solution

Step 1. Given information.

given,

Political view	Frequency
Liberal	147
Moderate	237
Conservative	116

Step 2. (a)  Let's identify the population.

Population:

The population is a complete set of people considered in the study.

Therefore, the number of people in the study was "new college students entering American Freshman".

Now, Identify the variable in the study.

A variable is an attribute or attribute that can be measured. The amount of flexibility may vary for each unit. That is, the variable is defined as the element recorded in each case.

From the given definition, the variables under the study "Political Perspective" because the outcome of each effort can be measured and this number may vary from effort to individual.

Step 3. (b)  Check whether the data provide sufficient evidence to conclude that this year's distribution of political ideas to college graduates has changed since the 2000 distribution in total.

The hypotheses are given below:

The null hypothesis is:

$H_0$: There is no evidence that the distribution of political views for this year's incoming college freshmen has changed from the 2000 distribution.

An alternative hypothesis is:

$H_1$ : The distribution of political views for this year's incoming college freshmen has changed from the 2000 distribution.

Step 4. Let's use the MINITAB to obtain the test statistic and p-value.

MINITAB procedure:

Step 1: Choose Stat > Tables > Chi-Square Goodness of Fit Test (One Variable).
Step 2: In Observed counts, enter the column$"O"$.
Step 3: In Category names, enter the column "View".
Step 4: Under Test, select the column of $"P"$in Specific proportions.

Step 5: Click ok.

Step 5. MINITAB output:

According to the output, the value of the test statistic is $4.39410$and the p-value is $0.111$.

Step 6. Conclusion for 5% significance level:

p-value is greater than the level of significance.

That is, p-value $(=0.111)>\alpha (=0.05)$.

Therefore, the null hypothesis is not rejected at the localid="1651991880138" $5\%$level.

So, the data do not provide sufficient evidence that concluded this year's distribution of political views for incoming college freshmen has changed from the 2000 distribution at a $5\%$level of significance

Step 7. (c)  Now, Conclusion for  significance level:

the p-value is greater than the significance level.

That is p-value $(=0.111)>\alpha (=0.10)$.

Thus, the null hypothesis is not rejected at the $10\%$level.

So, the data do not provide sufficient evidence to conclude that this year's distribution of political views for incoming college freshmen has changed from the 2000 distribution at a $10\%$level of significance.