Question

To determine whether the pipe welds in a nuclear power plant meet specifications, a random sample of welds is selected, and tests are conducted on each weld in the sample. Weld strength is measured as the force required to break the weld. Suppose the specifications state that mean strength of welds should exceed 100 lb/sq in; the inspection team decides to test    H0 ;    μ=100 versus Ha    ;μ > 100.+  Explain why it might be preferable to use this    Ha rather than μ+ < +100.

Answer 1

Concepts and reason

To make decisions or judgments about the value of a parameter, such as a population mean is known as inferential statistics. One of the most commonly used methods for making such decisions or judgments are to perform a hypothesis test.

A hypothesis testing is used to make inferences about the population based on the sample data. The hypotheses test consists of null hypothesis and alternative hypothesis.

Fundamentals

The null hypothesis states that there is no difference in the test, which is denoted by. Moreover, the sign of null hypothesis is equal, greater than or equal and less than or equal.

The hypothesis that differs from the null hypothesis is called alternative hypothesis. This signifies that there is a significant difference in the test. The sign of alternative hypothesis is less than, greater than, or not equal.

The objective is to test whether mean strength of welds should exceed 100

From the given information,

Let represent the mean strength of welds.

Null hypothesis:

The mean strength of welds does not exceed 100

Alternative hypothesis:

The mean strength of welds exceed 100

The null hypothesis and alternative hypotheses are,

The alternative hypothesis was chosen to be rather than since the inspection team wants sufficient evidence to support that the mean strength of welds exceeds 100

Ans:

The null hypothesis and alternative hypotheses are,