1. Topic 20 Examples
Check of Answers

2. 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

3. 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

4. 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 $ 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, The mean family income level in a city is $12,250
Ha: µ<12, The mean family income level in a city is less than $12,250

5. 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.

6. 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.

7. 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.