Notes 9.1, 9.4 - Part II

Calculator for Proportions  Stat  Tests  1-PropZTest (#5) MAT 1450 – Introduction to Statistics OS Chapter 9.1 – Null and Alternative Hypothesis OS Chapter 9.4 – Rare Events, the Sample, Decision and Conclusion MOM #18 Hypothesis Testing (p value approach) Step 1 Determine hypothesis & Sketch  Null hypothesis will always be μ = ¿  Alternative hypothesis is what is being tested Step 2 Find significance level  If none is stated, use α = 0.05 Step 3 Find test statistic using appropriate formula  z 0 when σ is known  t 0 when σ is unknown  z 0 for proportions  z 0 for comparing two independent means Step 4 Find the p value using your calculator Step 5 Compare p value and significance level to decide  If p < α , reject the null hypothesis  If p > α , fail to reject the null hypothesis Step 6 Interpret results  Write a sentence to answer the question A hypothesis test using proportions will assess whether or not a sample proportion represents the true proportion of the entire population. Test Statistic for Proportions: Ex. Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in 1

Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. 63 said they smoked to stay thin. Is there good enough evidence that more than 30% of the teen girls smoke to stay thin? Ex. A renowned marketing executive claimed that only 10% of customers are satisfied with their recent purchase. A survey conducted by a consumer association, involving a sample of 500 customers, found that 15% of them reported being satisfied with their purchases. Test the 2

regular physical exercise. Use a 0.05 significance level to test the claim that the percentage of students engaging in regular physical exercise has increased. 4