Topic 20 Examples Check of Answers

A test of significance for a population mean (with σ unknown) At the bakery where you work, loaves of bread are supposed to weigh 1 pound. You believe that new personnel are producing loaves that are heavier than 1 pound. As supervisor of quality control, you want to test your hypotheses at the 5% significance level. You decide to take a random sample of 20 loaves, and you obtain a mean weight of 1.05 pounds, with a standard deviation of 0.13 pounds. Perform the test of significance. A test of significance for a population mean (with σ unknown) Random sample from pop.? Stated random n≥30 or pop. normal? n=20 and pop. unknown n<30 and sample data approx. normal? Data unknown Results may be questionable. Ho: µ=1 The mean weight of a loaf of bread is 1 pound. Ha: µ>1 The mean weight of a loaf of bread is greater than 1 pound. Test Statistic: P(t19 > 1.72) = .0508 = 1.72

P-value ≈ α either decision would be OK At the bakery where you work, loaves of bread are supposed to weigh 1 pound. You believe that new personnel are producing loaves that are heavier than 1 pound. As supervisor of quality control, you want to test your hypotheses at the 5% significance level. You decide to take a random sample of 20 loaves, and you obtain a mean weight of 1.05 pounds, with a standard deviation of 0.13 pounds. Perform the test of significance. Because the p-value is larger than 5%, I fail to reject the null hypothesis. I do not have strong enough evidence to conclude that the mean weight of a loaf of bread is greater than 1 pound. P-value ≈ α either decision would be OK

Test of significance for a population mean (with sigma known) A local chamber of commerce claims that the mean family income level in a city is $12,250 with a standard deviation of $3180. An economist, thinking that the claim is too high, runs a hypothesis test, using a sample of 135 families, and finds a mean of $11,500. Should the chamber of commerce readjust their claim? Test of significance for a population mean (with sigma known) Requirements: Random sample from pop.? Not stated (assume random??) n≥30 or pop. normal? n = 135 Results should be valid. Ho: µ=12,250 The mean family income level in a city is $12,250 Ha: µ<12,250 The mean family income level in a city is less than $12,250

Continued… Because the p-value is less than 5% (alpha), we reject the null hypothesis and state there is strong enough evidence to conclude that the mean family income level in this city is less than $12,250.

Test of significance for a population mean (with sigma unknown) Great white sharks are big and hungry. The lengths in feet of 44 great whites are in a list that you have been given. Is there significant evidence at the 5% level to reject the claim “Great white sharks average 20 feet in length.”? Test of significance for a population mean (with sigma unknown) Requirements: Random sample from pop.? Not stated, unknown n≥30 or pop. normal? n = 44 Results may be questionable. Ho: µ=20 Great white sharks average 20 feet in length. Ha: µ≠20 Great white sharks do not average 20 feet in length.

Continued… with df = 43 Because the p-value is less than 5%, we reject the null hypothesis and state that there is strong enough evidence to conclude that great white sharks do not average 20 feet in length.