For the hypothesis test H0: μ=10 against H1: μ>10 with variance unknown and n=15, approximate th

step 1 Hello, welcome to this lesson. In this lesson, we're looking for the P value. We have the altern

For the hypothesis test H0: μ=10 against H1: μ>10 with...

Key Concepts

Test Statistic

A test statistic is a standardized value calculated from sample data during a hypothesis test. It is used to determine whether to reject the null hypothesis. In the context of a t-test, the test statistic follows a t-distribution under the null hypothesis, and its magnitude relative to the critical values derived from the t-distribution helps in making a statistical decision.

Hypothesis Testing

Hypothesis testing is a statistical method used to decide whether there is enough evidence in a sample of data to infer that a certain condition holds for the entire population. It involves setting up a null hypothesis (H0), which represents a baseline claim, and an alternative hypothesis (H1), which represents a new claim. The outcome of the test helps determine if the data provide sufficient evidence to reject the null hypothesis in favor of the alternative.

t-Distribution

The t-distribution is a probability distribution that arises when estimating the mean of a normally distributed population in situations where the sample size is small and the population standard deviation is unknown. It is similar to the normal distribution but has heavier tails, meaning it is more prone to producing values that fall far from its mean, which makes it more appropriate for inference in small samples.

P-value

The P-value is a probability that measures the strength of evidence against the null hypothesis. It represents the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. A smaller P-value indicates stronger evidence against the null hypothesis, guiding the decision on whether to reject the null hypothesis.

Degrees of Freedom

Degrees of freedom refer to the number of independent values or quantities that can be assigned to a statistical distribution that are free to vary. In the context of a t-test for a sample mean, the degrees of freedom are calculated as the sample size minus one (n-1). This adjustment is necessary because one parameter (the sample mean) is estimated from the data.

One-sided Test

A one-sided test is a type of hypothesis test in which the alternative hypothesis specifies that the parameter of interest is either greater than or less than the value stated in the null hypothesis, but not both. In such tests, the rejection region is located entirely in one tail of the probability distribution corresponding to the specified direction of the alternative hypothesis.

Transcript

00:01 Hello, welcome to this lesson.

00:03 In this lesson, we're looking for the p value.

00:08 We have the alternate hypothesis as the mean greater than 10.

00:12 That means we're dealing with the upper tail.

00:16 So the p value with the probability that the bigger t that we found from the table with a degree of freedom of n minus 1 is greater than the t value.

00:33 The t value.

00:33 The t.

00:35 Statistic that's given to us so now 2 .05 giving a degree of freedom of 14 that is here so 2 .05 is between 1 .7161 and 2 .15 and 2 .15 and that is 0 .0 between 0 .05 and 0 .025 and 0 .05 and 0 .25 so looking at it is way closer to 2 .145.

01:26 So we can have 0 .05, 7 like this.

01:36 0 .05, 0 .025.

01:41 So between this.

01:42 So you can say the p value is opposed really 0 .04 or something.

01:51 Because it's probably 2 .3.

01:54 Of course, it's very close to 2 .0 .025.

02:02 Alright, let's do with the second part where we have negative 1 .84.

02:17 So this one will take this one is less than around zero.

02:27 We're dealing with the positive side.

02:35 We are dealing with the upper side.

02:36 So this is around zero...