Question

Use the given information to find the P - value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis).

With H1 : p ≠ 3/5, the test statistic is z = 0.78. 

Answer 1

Concepts and reason

A statistical hypothesis is conjecture about a population parameter. The conjecture may or may not be true.

There are two types of statistical hypothesis which are null hypothesis and alternative hypothesis.

The null hypothesis is a statistical hypothesis that states that there is no difference between two parameters. The signs of null hypothesis can be represented as

The alternative hypothesis is a statistical hypothesis that states that there is difference between two parameters. The signs of alternative hypothesis can be represented as

Hypothesis testing for single proportion is used to test whether the sample proportion is a good factor to the population proportion or not.

The p-value provided information about the amount of statistical evidence that supports the alternative hypothesis.

The p-value of a test is the probability of observing a test statistic at least as extreme as the one computed, given that the null hypothesis is true.

Fundamentals

The excel formula for determining the value is,

$2P(Z >\z)) = 2[1- P(Z = z)] (One-tailed test) = 2[1-(NORMSDIST (2))] $

Decision rule: Reject if otherwise do not reject

From the information,

Claim: The population proportion is not equals to

The z-test statistic is,$z=0.78 $

Level of significance,

The value is,

From step (1), the value is 0.4354.

Compare the p-value with the level of significance.

From the values of p-value and level of significance, the value is greater than the level of significance. Hence, there is no enough evidence to reject the null hypothesis.

Ans:

The value is 0.4354. Fail to reject for the given level of significance.