What do you mean by type 1 error and Type 2 error?

In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a “false positive” finding or conclusion; example: “an innocent person is convicted”), while a type II error is the mistaken acceptance of an actually false null hypothesis (also known as a ” …

What is the formula for P value?

The p-value is calculated using the sampling distribution of the test statistic under the null hypothesis, the sample data, and the type of test being done (lower-tailed test, upper-tailed test, or two-sided test). The p-value for: a lower-tailed test is specified by: p-value = P(TS ts | H 0 is true) = cdf(ts)

What formula is used to calculate the degrees of freedom for the t test for comparing two population means when the population variances are unknown and unequal?

In the test for comparing two population means when population variances are unknown and unequal, a student calculates the degrees of freedom using the proper formula as 65.3. Let µD denote the mean of the difference: score after tutoring minus score before tutoring.

When N 30 and the population standard deviation is not known what is the appropriate distribution?

t-distribution table
Main Point to Remember: You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct.

What is Type 2 error in statistics?

A type II error is a statistical term used within the context of hypothesis testing that describes the error that occurs when one accepts a null hypothesis that is actually false. This is a type II error because we accept the conclusion of the test as negative, even though it is incorrect.

How do you find the p-value in hypothesis testing?

Graphically, the p value is the area in the tail of a probability distribution. It’s calculated when you run hypothesis test and is the area to the right of the test statistic (if you’re running a two-tailed test, it’s the area to the left and to the right).

How do you calculate p-value by hand?

Example: Calculating the p-value from a t-test by hand

1. Step 1: State the null and alternative hypotheses.
2. Step 2: Find the test statistic.
3. Step 3: Find the p-value for the test statistic. To find the p-value by hand, we need to use the t-Distribution table with n-1 degrees of freedom.
4. Step 4: Draw a conclusion.

What test statistic will be used if the sample size is above 30?

Z-Tests
Understanding Z-Tests The z-test is best used for greater-than-30 samples because, under the central limit theorem, as the number of samples gets larger, the samples are considered to be approximately normally distributed.

What is NP and NQ?

When testing a single population proportion use a normal test for a single population proportion if the data comes from a simple, random sample, fill the requirements for a binomial distribution, and the mean number of success and the mean number of failures satisfy the conditions: np > 5 and nq > n where n is the …

What is the sample distribution of the sample mean?

The Sampling Distribution of the Sample Mean If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).

What is the sampling distribution of X-bar?

The distribution of the values of the sample mean (x-bar) in repeated samples is called the sampling distribution of x-bar. Did I Get This?: Simulation #3 (x-bar)

What is the probability that the sample mean is greater than 102?

The probability that the sample mean is greater than 102 depends on the population distribution. For example, suppose 2\% of the population has value 37 and the other 98\% has value 101 2/7, then the mean is 100, the variance is 81, but no sample of any size will ever have a mean above 102.

How do you find the sample variance of a random sample?

X 1, X 2, …, X n are observations of a random sample of size n from the normal distribution N (μ, σ 2) X ¯ = 1 n ∑ i = 1 n X i is the sample mean of the n observations, and S 2 = 1 n − 1 ∑ i = 1 n (X i − X ¯) 2 is the sample variance of the n observations.