Statıstıcs Iı

Yanıt Açıklaması: 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 (H 0 ) when it is actually false. (False, type I error is defined as rejecting the null hypothesis (H 0 ) when it is actually true.) III.  Type II error is defined as rejecting the null hypothesis (H 0 ) when it is actually true. (False, type II error is defined as failing to reject the null hypothesis (H 0 ) when it is actually false.) The answer is A.

Yanıt Açıklaması: Population can be finite or infinite.

Yanıt Açıklaması: 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.

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

Yanıt Açıklaması: 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 A 2 = 25, s B 2 = 16. Therefore [(25/250)+(16/160)] = 1/5. The test statistic z=5/(1/5)=25 The answer is B.

Yanıt Açıklaması: 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.

Yanıt Açıklaması: 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.

Yanıt Açıklaması: A population is the universe to be sampled, such as all Turkish people, all universities in Turkey, all pregnant women over 40 years of age, all adult males who smoke 20 cigarettes or more daily, or all the buildings in Eskişehir, Turkey.

Yanıt Açıklaması: 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.

Yanıt Açıklaması: 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: H 0 : µ 1 = µ 2 or H 0 : µ 1 – µ 2 = 0 H 1 : µ 1 > µ 2 or H 1 : µ 1 – µ 2 > 0 The answer is E.

Yanıt Açıklaması: 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.

Yanıt Açıklaması: 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.

Yanıt Açıklaması: Stratums are used in stratified sampling.

Yanıt Açıklaması: 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.

Yanıt Açıklaması: a hypothesis test which is a decision-making process that uses sample statistics to test a claim or assumption about the value of a population parameter. These claims or assumptions about the population parameter could be known standard values and they may or may not be true. In that case statistical hypothesis testing denotes the formal processes used by statisticians to accept or reject the statistical hypotheses.

Yanıt Açıklaması: If the null hypothesis (H0) is rejected in a hypothesis test with the significance level α then it is said that statistical hypothesis test results are statistically significant at the α level. Determination of the significance level is specifying the rejection probability of the null hypothesis (H0) when it is actually true. The significance level α of a hypothesis test is determined by the researcher before the data collection. Often the level of significance α value of a hypothesis test is selected as 1%, 5% or 10%. When you choose the significance level, on practice, it means that if you repeatedly create many samples from the population in question, 1% of the time your results will not be correct.

Yanıt Açıklaması: 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

Yanıt Açıklaması: 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.

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

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