1. A weight loss program claims that program participants have a mean weight loss of at least 10 pounds after one month. You work for a medical association and are asked to test this claim. From a random sample of 30 program participants you find a mean weight loss of 9.8 pounds and a standard deviation of 2.4 pounds. At α = 0.03, how will you respond to the program’s claim? Fail to reject H0. There is insufficient evidence to reject the claim.

2. Sec. 7.3 Hypothesis Testing (small samples)
Mr. Ricks
Madison High School

3. t-Distributions
Used when n < 30 and population has a normal distribution (or near normal)
Symmetrical and bell-shaped but have thicker tails (the fewer samples the thicker the tail)
Rely on degrees of freedom
d.f. = n – 1, as d.f. increases, the curve approaches the Standard normal curve

5. Finding critical values (t0) in a t-distribution
Identify the α
Identify the degrees of freedom d.f. = n – 1
Find the critical value(s) using table on pg. A18 in book or on calculator (2nd  DISTR4)

6. Find the critical value t0 for a left-tailed test with α = 0
Find the critical value t0 for a left-tailed test with α = 0.01 and n = 14.

7. Find the critical value t0 for a right-tailed test with α = 0
Find the critical value t0 for a right-tailed test with α = 0.05 and n = 9.

8. Find the critical values ±t0 for a two-tailed test with α = 0
Find the critical values ±t0 for a two-tailed test with α = 0.01 and n = 16.

9. t-Test for a mean μ Used when population is normal or nearly normal
σ is unknown and n < 30
The test statistic is 𝑥 and the standardized test statistic is t
𝑡= 𝑥 −𝜇 𝑠/ 𝑛
d.f. = n – 1

10. Using t-Test for a Mean μ (small sample)
State claim, H0, and HA
Identify α
Identify d.f.
Determine critical value(s) t0 and rejection regions
Find t
Make a decision and interpret in context of the original claim

11. An insurance agent says that the cost of insuring a 2015 Ford F-150 is at least $875. A random sample of nine similar insurance quotes has a mean cost of $825 and a standard deviation of $62. Make a decision at α = t0 = , t = so fail to reject H0

12. An industrial company claims the mean pH level of the water in a nearby river is 6.8. You randomly select 19 water samples and measure the pH of each. The sample mean and standard deviation are 6.7 and Make a decision based on α = t0 = ±2.101, t = so fail to reject H0

13. Sec. 7.3 Pg. 356 #3-15,17,19-23,25,27,28,37,38 24 Problems