Statistics 2 Dersi 3. Ünite Sorularla Öğrenelim

What is a parameter?

A parameter is a value that defines the characteristic of a whole population which means that population parameter consists of mean, variance, standard deviation, mode, median or proportion of the population or objects under consideration.

What is a statistical hypothesis? 

A statistical hypothesis is a statement about a population parameter. Researchers and scientists in various areas for instance business, marketing, medicine, agriculture and education utilize hypothesis testing to make decisions about the population parameters based on sample information.

What is a hypothesis?

In general, a hypothesis is a proposition for the specific situation encountered.

What are the steps of hypothesis testing?

Step 1: State null and alternate hypotheses
Step 2: Select a level of significance
Step 3: Identify the test statistic
Step 4: Formulate a decision rule
Step 5: Take a sample and make the decision

Define the null and alternate hypotheses briefly.

Every statistical hypothesis-testing process begins with the statement of a hypothesis. There are two types of statistical hypotheses for each circumstance. These hypotheses are the null hypothesis and the alternative hypothesis which are denoted by H0 and H1 respectively. The null hypothesis H0 is a statistical statement which specifies that there is a specific value of a population parameter. Generally thought as the status quo. It is what you already know about the population parameter. On the other hand, the alternative hypothesis H1 specifies that there is a difference between the value of a population parameter and a certain value. Alternative hypothesis is also called as research hypothesis since the alternative hypothesis defines what the decision maker’s conclusion is if he/she rejects the null hypothesis.

What is a Type I error?

Type I error is defined as rejecting the null hypothesis when it is actually true.

What is a Type II error?

Type II error is defined as failing to reject the null hypothesis when it is actually false.

In a study the significance level is 0.05. What would be the confidence level of this study?

The confidence level of this study would be 0.95.

If the observed value of the test statistic is greater than the theoretical value of the test statistic, what is the decision in hypothesis testing?

In this case, the decision in hypothesis testing is to 'Reject the Null hypothesis'. 

What is the mathematical sign used in the null hypothesis between parameter and a value?

It is the equal (=) sign. 

If observed z value is 3.68 and the theoretical z value from the standard normal distribution table is 1.96 in a study, what should be the decision about the null hypothesis?

The null hypothesis should be rejected in this case. 

In hypothesis testing procedure, the mean of the population is tested, calculate is the theoretical z value from standard normal distribution for a twosided test where the significance level ? = 0.10?

The z value from standard normal distribution would be 1.65. 

In a hypothesis testing procedure, the population arithmetic mean is 1200 and population standard deviation is 200, sample arithmetic mean of a random sample of 144 observations is 1100. If this procedure is followed, what is the value of the observed z?

The value of the observed z would be 5.998 in this case.

If a sample with 16 observations has a mean of 28, standard deviation of 4, and the population mean is 25, then what is the observed t value in a hypothesis testing procedure?

The observed t value would be 33 in this specific case.

In a classroom there are 50 students. Out of these 50 students 30 of them are male. If a hypothesis testing procedure for the population proportion of female students is to be created, what is the value of the sample proportion of the female students?

The value of the sample proportion of the female students is 0.40.

If a population proportion is 0.50 and a sample, taken randomly from this population, proportion is 0.60, and the sample size is 125 then what is the value of observed z?

The value of observed z would be 2.24 in this case.