It is about the hypothesis testing., Cheat Sheet of Mathematics

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Hypothesis

Testing

Statistics

Statistics

Identify the null and alternative hypotheses.

Compute the test statistic.

Find the critical value.

Make a statistical decision.

Summarize the results.

Steps in Hypothesis Testing

Try this!

A test in Statistics was given to two groups of

Business Administration students. 25 students

majoring in Finance got an average score of 78 with

a standard deviation of 3.5, while 25 students

majoring in Management got an average of score of

81 with a standard deviation of 2.5. Do the

performance of the two groups differ? Assume that

the distribution is normal. Use alpha of 1%.

Try this!

In order to increase customer service, a muffler

repair shop claims its mechanics can replace a

muffler in 12 minutes. A time management

specialist selected six repair jobs and found their

mean time to be 11.6 minutes. The standard

deviation of the sample was 2.1 minutes. At 0.

level of significance, is there enough evidence to

conclude that the mean time in changing is less

than 12 minutes?

Statistics

Identify the null and alternative hypotheses.

Compute the test statistic.

Find the p-value.

Make a statistical decision.

Interpret the results.

Steps in Hypothesis Testing

P-value Approach

P-value Interpretation Less than 0.01 Highly statistically significant There is very strong evidence against H 0 0.01 to 0.05 Statistically significant Adequate evidence against H 0 Greater than 0.05 Insufficient evidence against H 0

Identify the null and alternative hypotheses.

The LA Company has developed a new battery. Its engineering department claims that each battery lasts for 200 minutes. In order to test this claim, the company selected a random sample of 100 new batteries so that this sample has a mean of 196 minutes with a standard deviation of 30 minutes. Test the claim that the new batteries run with an average of 200 minutes. Use a 0.05 level of significance.

H

: H

a

The new batteries will last for 200 minutes. The new batteries will not last for 200 minutes.

Compute the test statistic. The LA Company has developed a new battery. Its engineering department claims that each battery lasts for 200 minutes. In order to test this claim, the company selected a random sample of 100 new batteries so that this sample has a mean of 196 minutes with a standard deviation of 30 minutes. Test the claim that the new batteries run with an average of 200 minutes. Use a 0.05 level of significance. 𝑧 = 𝑥 − 𝜇 𝑠 √ 𝑛 ¿ 196 − 200 30 √^100 ¿ − 𝟏. 𝟑𝟑

Make the decision. The LA Company has developed a new battery. Its engineering department claims that each battery lasts for 200 minutes. In order to test this claim, the company selected a random sample of 100 new batteries so that this sample has a mean of 196 minutes with a standard deviation of 30 minutes. Test the claim that the new batteries run with an average of 200 minutes. Use a 0.05 level of significance.

Reject H

Do not Reject H

:

Make the decision. The LA Company has developed a new battery. Its engineering department claims that each battery lasts for 200 minutes. In order to test this claim, the company selected a random sample of 100 new batteries so that this sample has a mean of 196 minutes with a standard deviation of 30 minutes. Test the claim that the new batteries run with an average of 200 minutes. Use a 0.05 level of significance. 0_._ 1836 > 0_._ 05 Decision: Do not Reject H 0

Try this!

Bryan administered a mathematics achievement

test to a random sample of 50 graduating students.

In this sample, = 90, = 10. The population

parameters are = 83 and

1. Does the sample come from the average

population?

2. Is the performance of the sample above

average?

Use and the p-value method.