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
In a hypothesis testing process, the alternative hypothesis is written as two-sided, therefore the rejection area of the hypothesis testing is in the either side of the distribution. If the sampling distribution is Normal and the significance level is 0.05, what are the critical values to test the claimed hypothesis is true?
In a hypothesis testing problem, population standard deviation of the variable is 100 and the variable follows a normal distribution with an arithmetic mean of 1000. A sample of 125 objects are randomly chosen and the values of the objects for the variable are recorded. The sample arithmetic mean of the variable is 940, if the level of significance is α = 0.05, if you follow the five step hypothesis testing procedure what is the value of observed or sample z value?
We need to calculate the observed z value as follows:
In an investigation, the population proportion for a variable is known as 0.02. This morning the quality control manager wants to check if this population proportion still holds. Therefore, he takes a sample of 60 products and the outcome of the variable is seen on 4 products. If the quality control manager creates a hypothesis testing procedure in this problem, what is the observed z value?
We need to calculate the observed z value as follows:
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.
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.
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.
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 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.
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 α = 0.10?
The z value from standard normal distribution would be 1.65.
Solve the following equation:
The result of the equation is 11.54.
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.