I. There are four possible correct and incorrect decision-making situations that may occur through statistical hypothesis testing. (True)

II. Type I error is defined as failing to reject the null hypothesis (H₀) when it is actually false. (False, type I error is defined as rejecting the null hypothesis (H₀) when it is actually true.)

III.  Type II error is defined as rejecting the null hypothesis (H₀) when it is actually true. (False, type II error is defined as failing to reject the null hypothesis (H₀) when it is actually false.) 

The answer is A.

The most basic sampling method is the simple random sampling. The simple random sample from a population is a sample that is selected so that each possible sample combination of the specified size has equal probability of being chosen. In practice, a simple random sample is usually called random sample. Random numbers are often used to select simple random samples from a population frame. The correct answer is C.

If ?=0.05, then the area between z=0 and the critical value of z must be (1-0.05)/2=0.4775, which corresponds to z=1.96

The independent random sample sizes are n_A = 250 students and n_B = 160 students. Also, the class (A) mean test score is x_A = 70 and standard deviation s_A = 5, and the class (B) mean test score is x_B = 65 and standard deviation s_B= 4. Then, the test statistic can be obtained as follows: x_A - x_B = 70 - 65 = 5, s_A² = 25, s_B² = 16. Therefore [(25/250)+(16/160)] = 1/5. The test statistic z=5/(1/5)=25

The answer is B.

The null hypothesis (H0 ) is “the mean weight of the packages is 450 grams” and the alternative hypothesis (H1 ) is “the mean weight of the packages is less than 450 grams”. The correct answer is B. 

The simple random sample from a population is a sample that is selected so that each possible sample combination of the specified size has equal probability of being chosen. In practice, a simple random sample is usually called random sample.. pg. 7 . Correct answer is D.

The steps in hypothesis testing are summarized below. 1. Determine the population proportion under study and form the null hypothesis (H0 ) and the alternative hypothesis (H1 ). 2. Choose the level of significance ?. 3. Calculate the test statistic z for proportions. 4. Identify the critical points and critical region for the hypothesis test. 5. Based on sample information decide to reject or fail to reject the null hypothesis (H0 ) and interpret the results of the hypothesis test. Thefore, the correct answer is B. 

 Since the claim in the question is the first group’s mean is greater than the second group, the alternative hypothesis is right-tailed (right sided). Then the hypothesis can be expressed as follows:

H₀ : µ₁ = µ₂  or H₀: µ₁ – µ₂ = 0
H₁: µ₁> µ₂ or H₁: µ₁ – µ₂ > 0

The answer is E.

Populations can be heterogenous or infinite. So arguments in A and B are not true. Population size is larger than the sample, so C is false also. There is no restriction on population size, so D is false. However, populatios can contain any type of objects. So E is true.

Hypothesis tests for proportions can be used if the parameter of interest is a proportion of a population in which there are two different categories. Such as, mid-term results of students who have a score below or above fifty, or quality engineers test the proportion of parts that are defective or not defective. From these examples, it is clear that the statistical hypothesis test involving a proportion of the population can be considered as a binomial experiment since there are two outcomes.  The correct answer is B. 

Stratums are used in stratified sampling.

The null hypothesis is that the average grades are same (X=Y) and the alternative is that they are not same (X≠Y). So the answer is choice E.

The test statistic for a one-way ANOVA test is the ratio of two variances; namely the variance between samples (MSB) and variance within samples (MSW). Then, the test statistic F can be obtained as follows, F = MSB/MSW. Therefore F=10/20 = 0.5

The test statistic for a one-way ANOVA test is the ratio of two variances; namely the variance between samples (MSB) and variance within samples (MSW). Then, the test statistic F can be obtained as follows, F = MSB / MSW.  

Then, 

2 = 200/ MSW 

So, the variance within samples is 100.  

In cluster sampling the subgroups occur naturally. These subgroups are called clusters.

x = 240.000 . 0.25 + 260.000 . 0.30 = 138.000. pg. 3. Correct answer is C.