1.Shahla is the manager of the quality control unit of a production line. She suspects that his products do not meet the length criteria. In particular, she thinks that the length of the products are bigger than 18 cm. She takes a simple random sample of products and performs a statistic test to confirm whether the products are meeting the max limit of 18 cm.

What would be the null and alternative hypothesis for this research?

2.A simple random sample of 25 top movies is taken from a movie website and the average lengths of movies are found to be 150 min. The population standard deviation is known to be 10 min.

a.Test the hypothesis that the population mean length is greater than 145 min using the 0.05 level of significance.

b.Test the hypothesis that the population mean account balance is different from 155 min using the critical value approach and a 0.05 level of significance.

3.A simple random sample of 20 customers is taken from a customer information file and the average age is 27. The sample standard deviation s is found to be 1.5.

a.Test the hypothesis that the population mean age is less than 29 using the critical value approach and a 0.10 level of significance.

b.Test the hypothesis that the population mean age is different from 30 using the 0.05 level of significance.

4.The proportion of basketball players who have not had a missed shot in MBA last year is 27 out of a sample of top 60 players.

Hint: The standard deviation of population and the standard deviation of the sample are unknown, thus you have to use the square root of p(1-p)/n as a best estimate of the standard deviation.

a.Test the hypothesis that the population proportion of basketball players who have not had a missed shot in MBA last year is greater than 0.42 using the critical value approach and a 0.05 level of significance.

b.Test the hypothesis that the population proportion of customers who are completely satisfied is different from 0.5 using the p-value approach and a 0.05 level of significance.

5.The distance in meters that a shoe can be used before first signs of wearing appears on it is taken from two samples of two top types of shoes from a brand. The chain wants to use this data to test the research (alternative) hypothesis that the mean distance for type 1 is lower than that of type 2.

Hint: (You can use excel to calculate mean and std. dev.)

Type 1 (in meters)

Type 1 (in meters) Type 2 (in meters)

250 269

367 312

181 267

299 245

185 239

111 261

192 288

283 307

225

The average for sample 1 is 232.56 and for sample 2 is 273.5. The std. dev. for sample 1 is 76.43 and is 26.82 for sample 2.

a.What are the null and alternative hypothesis for this research?

b.Compute the test statistic t used to test the hypothesis. Note that the population standard deviations are not known and therefore you cannot use the formula in Section 10.1 of your text book. Use the one in Section 10.2 instead.

c.Compute the degree of freedom for the test statistic t.

d.Can the chain conclude that the mean distance for type 1 is lower than that of type 2? Use the critical-value approach and = 0.05 to conduct the hypothesis test.

e.Construct a 95% confidence interval for the difference of mean distance for the two types.

6.To compare prices of two local stores, a random sample of items that are sold in both stores were selected and their price noted in the first weekend of the year:

Item Store A Store B Difference (Store A - Store B)

1 1.65 1.99 -0.34

2 8.70 8.49 0.21

3 0.75 0.90 -0.15

4 1.05 0.99 0.06

5 11.30 11.99 -0.69

6 7.70 7.99 -0.29

a.What are the null and alternative hypothesis if we want to confirm that on average, prices at Store 1 is different from the prices at Store 2, that is, the difference is different from 0?

b.What are the sample mean difference in prices and the sample standard deviation?

c.Compute the test statistic t used to test the hypothesis.

d.Compute the degree of freedom for the test statistic t

e.Can we conclude that on average, prices at Store 1 is different from the prices at Store 2? Use the critical-value approach and = 0.05 to conduct the hypothesis test.

f.Use the above data to construct a 95% confidence interval for the difference in prices between the two stores.

7.In a completely randomized design, 5 experimental units were used for each of the three levels of the factor.

Source of Variation Sum of Squares Degrees of Freedom Mean Square F

Treatment

Error 219.55

Total 1563.71

a.Complete the ANOVA table.

b.Find the critical value at the 0.05 level of significance from the F table for testing whether the population means for the three levels of the factors are different.

c.Use the critical value approach and = 0.05 to test whether the population means for the three levels of the factors are the same.

You can find the F-distribution in your text book at page 595 - 606 in appendix A.