Presentation on theme: "Hypothesis Testing for the Mean (Small Samples)"— Presentation transcript:
1Hypothesis Testing for the Mean (Small Samples) Section 7.3Hypothesis Testing for the Mean (Small Samples)
2Similar to section 7.2…When the distribution is normal (or nearly normal), n < 30 or σ is unknown.Use the t-distribution table:Degrees of freedom: d.f. = n – 1
3EX: find critical value, t0 Left tailed test, alpha = 0.01, n = 13Right tailed test, alpha = 0.10, n =10Two tailed test, alpha = 0.05, n = 22
4Guidelines for the t-Test find H0 and HaIdentify the level of significance, alphaIdentify the degrees of freedom, d.f.Find the critical value(s) using the table.Sketch the curve and shade the rejection region(s)Find tMake the decision to reject or not reject H0Interpret the decision in context.
5Use a t-test to test the claim 14. Claim: µ > 25, alpha = 0.05, sample mean = 26.2, s = 2.32, n = 1715. Claim: µ > 8000, alpha = 0.01, sample mean = 7700, s = 450, n = 25
620. A company claims that the mean battery life of their MP3 player is at least 30 hours. You suspect that the claim is incorrect and find that a random sample of 18 MP3 players has a mean battery life of 28.5 hours and a standard deviation of 1.7 hours. Is there enough evidence to reject the claim at alpha = 0.01?
726. A repair shop believes that people travel more than 3500 miles between oil changes. A random sample of 8 cars getting an oil change has a mean distance of miles since the last oil change with a standard deviation of 225 miles. At alpha = 0.05, do you have enough evidence to support the shop’s claim?
8HYPOTHESIS TESTING FOR PROPORTIONS Section 7.4HYPOTHESIS TESTING FOR PROPORTIONS
10Guidelines for the z-Test 1. find H0 and Ha2. identify alpha3. find the critical value(s)4. shade the rejection region(s)5. find z6. make decision to reject or not reject the null hypothesis7. interpret decision in context
11Determine if a normal distribution can be used. If so, test the claim. 4. Claim: p > 0.48, alpha = 0.08, sample proportion = 0.40, n = 908. Claim: p = 0.95, alpha = 0.10, sample proportion = 0.875, n = 50
1214. A research center claims that 16% of US adults say that curling is the Winter Olympic sport they would like to try the most. In a random sample of 300 US adults, 20% say that curling is the Winter Olympic sport they would like to try the most. At alpha = 0.05, is there enough evidence to reject the researcher’s claim?
1316. A humane society claims that 30% of US households own a cat 16. A humane society claims that 30% of US households own a cat. In a random sample of 200 US households, 72 say they own a cat. At alpha = 0.05, is there enough evidence to reject the society’s claim?