Presentation on theme: "Hypothesis Testing with ONE Sample"— Presentation transcript:
1 Hypothesis Testing with ONE Sample Chapter SevenHypothesis Testing with ONE Sample
2 Introduction to Hypothesis Testing Section 7.1Introduction to Hypothesis Testing
3 Hypothesis Tests… A process that uses sample statistics to test a claim about a population parameter.Test includes:Stating a NULL and an ALTERNATIVE Hypothesis.Determining whether to REJECT or to NOT REJECT the Null Hypothesis. (If the Null is rejected, that means the Alternative must be true.)
4 Stating a HypothesisThe Null Hypothesis (H0) is a statistical hypothesis that contains some statement of equality, such as =, <, or >The Alternative Hypothesis (Ha) is the complement of the null hypothesis. It contains a statement of inequality, such as ≠, <, or >
5 Left, Right, or Two-Tailed Tests If the Alternative Hypotheses, Ha , includes <, it is considered a LEFT TAILED test.If the Alternative Hypotheses, Ha , includes >, it is considered a RIGHT TAILED test.If the Alternative Hypotheses, Ha , includes ≠, it is considered a TWO TAILED test.
6 EX: State the Null and Alternative Hypotheses. 26. As stated by a company’s shipping department, the number of shipping errors per mission shipments has a standard deviation that is less than A state park claims that the mean height of oak trees in the park is at least 85 feet.
7 Types of ErrorsWhen doing a test, you will decide whether to reject or not reject the null hypothesis. Since the decision is based on SAMPLE data, there is a possibility the decision will be wrong. Type I error: the null hypothesis is rejected when it is true. Type II error: the null hypothesis is not rejected when it is false.
8 4 possible outcomes… TRUTH OF H0 DECISION H0 is TRUE H0 is FALSE Do not reject H0Correct DecisionType II ErrorReject H0Type I Error
9 Level of SignificanceThe level of significance is the maximum allowed probability of making a Type I error. It is denoted by the lowercase Greek letter alpha.The probability of making a Type II error is denoted by the lowercase Greek letter beta.
10 p-ValuesIf the null hypothesis is true, a p- Value of a hypothesis test is the probability of obtaining a sample statistic with a value as extreme or more extreme than the one determined from the sample data.The p-Value is connected to the area under the curve to the left and/or right on the normal curve.
11 Making and Interpreting your Decision Decision Rule based on the p-ValueCompare the p-Value with alpha.If p < alpha, reject H0If p > alpha, do not reject H0
12 General Steps for Hypothesis Testing State the null and alternative hypotheses.Specify the level of significance.Sketch the curve.Find the standardized statistic add to sketch and shade. (usually z or t-score)Find the p-ValueCompare p-Value to alpha to make the decision.Write a statement to interpret the decision in context of the original claim.
13 Hypothesis Testing for the MEAN (Large Samples) Section 7.2Hypothesis Testing for the MEAN (Large Samples)
14 Using p-Value to Make Decisions Decision Rule based on the p-ValueCompare the p-Value with alpha.If p < alpha, reject H0If p > alpha, do not reject H0
15 Finding the p-Value for a Hypothesis Test – using the table To find p-ValueLeft tailed: p = area in the left tailRight tailed: p = area in the right tailTwo Tailed: p = 2(area in one of the tails)This section we’ll be finding the z-values and using the standard normal table.
16 Find the p-value. Decide whether to reject or not reject the null hypothesis 4. Left tailed test, z = -1.55, alpha = 0.058. Two tailed test, z = 1.23, alpha = 0.10
17 Using p-Values for a z-Test Z-Test used when the population is normal, δ is known, and n is at least If n is more than 30, we can use s for δ.
18 Guidelines – using the p-value 1. find H0 and Ha2. identify alpha3. find z4. find area that corresponds to z (the p-value)5. compare p-value to alpha6. make decision7. interpret decision
19 30. A manufacturer of sprinkler systems designed for fire protection claims the average activating temperature is at least 135oF. To test this claim, you randomly select a sample of 32 systems and find mean = 133, and s = At alpha = 0.10, do you have enough evidence to reject the manufacturer’s claim?
20 Rejection Regions & Critical Values The Critical value (z0) is the z-score that corresponds to the level of significance (alpha)Z0 separates the rejection region from the non-rejection regionSketch a normal curve and shade the rejection region. (Left, right, or two tailed)
21 Find z0 and shade rejection region 18. Right tailed test, alpha = 0.0822. Two tailed test, alpha = 0.10
22 Guidelines – using rejection regions 1. find H0 and Ha2. identify alpha3. find z0 – the critical value(s)4. shade the rejection region(s)5. find z6. make decision (Is z in the rejection region?)7. interpret decision
23 38. A fast food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 920 milligrams. A random sample of 44 sandwiches has a mean sodium content of 925 with s = 18. At alpha = 0.10, do you have enough evidence to reject the restaurant’s claim?