Hypothesis Testing for the Mean (Small Samples) Section 7.3 Hypothesis Testing for the Mean (Small Samples)

Similar 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

EX: find critical value, t0 Left tailed test, α = 0.01, n = 13 Right tailed test, α = 0.10, n =10 Two tailed test, α = 0.05, n = 22

Guidelines for the t-Test find H0 and Ha Identify the level of significance, α Identify the degrees of freedom, d.f. Find the critical value(s) using the table. Sketch the curve and shade the rejection region(s) Find t Make the decision to reject or not reject H0 Interpret the decision in context.

Use a t-test to test the claim 14. Claim: µ > 25, α = 0.05, sample mean = 26.2, s = 2.32, n = 17 15. Claim: µ > 8000, α = 0.01, sample mean = 7700, s = 450, n = 25

18. 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?

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 3375 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?

HYPOTHESIS TESTING FOR PROPORTIONS Section 7.4 HYPOTHESIS TESTING FOR PROPORTIONS

Uses the z-Test

Guidelines for the z-Test np and nq both must be at least 5 1. find H0 and Ha 2. identify α 3. find the critical value(s) 4. shade the rejection region(s) 5. calculate z 6. make decision to reject or not reject the null hypothesis 7. interpret decision in context

Determine if a normal distribution can be used. If so, test the claim.  

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 α = 0.05, is there enough evidence to reject the researcher’s claim?

A research center claims that at most 75% of US adults think that drivers are safer using hands-free cell phones instead of using hand- held cell phones. In a random sample of 150 US adults, 77% think that drivers are safer using hands- free cell phones instead of hand- held cell phones. At α = 0.01, is there enough evidence to reject the center’s claim?