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Test of hypothesis using t statistics, ANOVA

1. Please define the following terms. Tell me how the term is used in statistics and provide an example to demonstrate your knowledge. Pasting a definition from the web or from the text will result in a zero for the final.

1.1 population proportion
1.2 type I error
1.3 p-value
1.4 ANOVA

2. The mean annual turnover rate of the 200-count bottle of Bayer Aspirin is 6.0 with a standard deviation of 0.50. (This indicates that the stock of Bayer turns over on the pharmacy shelves an average of 6 times per year.) It is suspected that the mean turnover has changed and is not 6.0. Use the .05 significance level.
(a) State the null hypothesis and the alternate hypothesis.
(b) What is the probability of a Type I error?
(c) Give the formula for the test statistic.
(d) State the decision rule.
(e) A random sample of 64 bottles of the 200-count size Bayer Aspirin showed a mean of 5.84. Shall we reject the hypothesis that the population mean is 6.0? Interpret the result.

3. A machine is set to fill a small bottle with 9.0 grams of medicine. A sample of eight bottles revealed the following amounts (grams) in each bottle.
9.2 8.7 8.9 8.6 8.8 8.5 8.7 9.0
At the .01 significance level, can we conclude that the mean weight is less than 9.0 grams?
(a) State the null hypothesis and the alternate hypothesis.
(b) How many degrees of freedom are there?
(c) Give the decision rule.
(d) Compute the value of t. What is your decision regarding the null hypothesis?
(e) Estimate the p-value.

4. The production manager at Bellevue Steel, a manufacturer of wheelchairs, wants to compare the number of defective wheelchairs produced on the day shift with the number on the afternoon shift. A sample of the production from 6 day shifts and 8 afternoon shifts revealed the following number of defects. At the .05 significance level, is there a difference in the mean number of defects per shift?
Day 5 8 7 6 9 7
Afternoon 8 10 7 11 9 12 14 9
(a) State the null hypothesis and the alternate hypothesis.
(b) What is the decision rule?
(c) What is the value of the test statistic?
(d) What is your decision regarding the null hypothesis?
(e) What is the p-value?
(f) Interpret the result.

5. Please complete the following table.

Source SS df MS F
treatment 2
error 17.43 1.245 xxxx
total 24.25 xxxx xxxx

6. Clean All is a new all-purpose cleaner being test marketed by placing displays in three different locations within various supermarkets. The number of 12-ounce bottles sold from each location within the supermarket is reported below. At the .05 significance level, is there a difference in the mean number of bottles sold at the three locations?

Near the bread 20 15 24 18
Near the beer 12 18 10 15
With other Cleaners 25 28 30 32

(a) State the null hypothesis and the alternate hypothesis.
(b) What is the decision rule?
(c) Compute the values of SS total, SST, and SSE.
(d) Develop an ANOVA table.
(e) What is your decision regarding the null hypothesis?

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Tests hypothesis using t statistics, ANOVA etc.

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