Stat 226 SI

4/9/13

“Hypothesis Testing”

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Part 1: Match the following terms with the most appropriate definition.

  1. Hypothesis
  2. Null Hypothesis
  3. Alternative Hypothesis
  4. T-statistic
  5. P-value
  6. Alpha (α)
  7. Type I Error
  8. Tyler II Error
  9. Statistical Inference

1.)The probability of rejecting the null hypothesis when the null hypothesis is true G

2.)The probability of obtaining a test statistic as unusual as the observed value, assuming the null hypothesis is true E

3.)The statement of what we assume to be true, denoted by H0B

4.)A claim or belief about a population parameter that we wish to test A

5.)The probability of failing to reject the null hypothesis when the null hypothesis is false H

6.)Based on information obtained from a sample, attempting to generalize what holds true for the entire population I

7.)A level of statistical significance, against which a p-value is tested F

8.)The number of standard errors below or above the mean the sample average is from the mean in the null hypothesisD

9.)The statement against what we assume to be true, denoted by HA C

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Part 2: A company that makes baby food claims that they fill the jars with 5 oz. of baby food. A random sample of 45 cans yielded a sample mean of = 4.9239 oz. We estimate the standard deviation equal to s = 0.6000 oz. To see if this company actually fills the jars less than 5 oz. full, conduct an appropriate test of hypothesis at the α = 0.01 level of significance.

A.)Set up the null and alternative hypothesis:

Ho: µ = 5Ha :µ < 5

B.)Calculate a t-statistic.

-0.851

C.)We obtain a p-value equal to 0.20. Interpret the p-value in terms of this problem.

Assuming the true average baby jar contains 5 oz. of food, there is a 20% probability of obtaining a test statistic of -0.851 or smaller.

D.)Make a decision about Ho.

p-value = 0.2 > alpha = 0.01  fail to reject Ho

E.)Write your conclusion.

At the alpha level of 0.01, we fail to reject the null hypothesis, which states the true mean amount of baby food is equal to 5 oz… we fail to find that the sample mean of 4.9239 is significantly different from the population mean 5.

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Part 3: Chevy manufactures the “Cruze,” which they claim gets 40 highway mpg on average. A sample of 49 Cruze cars yields a sample mean highway mpg of = 41.1589 and a standard deviation of s = 3 mpg. Is there evidence that suggests the average highway mpg for all Chevy Cruze cars is different from 40 highway mpg? Test this claim at the α = 0.05 level of significance.

Ho: µ=40Ha: µ 40

t = 2.704

p = 0.01 < alpha = 0.05  reject Ho

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Part 4: Divide yourselves into groups of 2. Create a problem similar to the ones just practiced for hypothesis testing. Then, trade your problem with another group and solve each other’s hypothesis test.