Descriptive Statistics: cal. Is it reasonable to use a t test to test hypotheses about the mean? Hypotheses: Test Statistic: P value:

Transcription

1 1. Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases. It is therefore important that the information be accurate. A random sample of n = 12 frozen dinners of a certain type was selected from production and the calorie content was determined. The resulting observations are: We are interested in testing to see if the true mean calorie content differs from the stated value of 240. Minitab gives the following descriptive statistics and histogram. 3 Descriptive Statistics: cal Variable N Mean Median TrMean StDev SE Mean cal Variable Minimum Maximum Q1 Q3 cal c y e n u q e Fr cal Is it reasonable to use a t test to test hypotheses about the mean? ST hw7

2 2. Suppose that in the previous problem they also measured the fat content of the 12 meals at the same time. They wish to test if the fat content is not equal to the stated value of 8 grams at the.05 significance level. Use the Minitab printout below to complete the following: One Sample T: fat Test of mu = 8 vs mu not = 8 Variable N Mean StDev SE Mean fat Variable 95.0% CI T P fat ( 8.029, 8.661) Decision based on the P value and reason for the decision. 3. In a study investigating the hourly rates of women in the workforce, a sample of 40 unionized women in manufacturing was obtained, resulting in a mean of $21.31 and a standard deviation of $1.95. A simple random sample of 30 non unionized women resulted in a mean hourly rate of $19.71 and a standard deviation of $2.19. Test at the.01 level whether the mean hourly rates are the same for the two groups. Answer the following by hand: ST hw7

3 Degrees of Freedom: Homework 7 Compute a (1 α)100% Confidence Interval for µ 1 µ 2 : Decision based on Confidence Interval and reason for the decision: Check your answers above with the following Minitab Printout: Two Sample T Test and CI: Union, Non Two sample T for Union vs Non N Mean StDev SE Mean Union Non Difference = mu Union mu Non Estimate for difference: % CI for difference: (0.283, 2.913) T Test of difference = 0 (vs not =): T Value = 3.22 P Value = DF = 68 Both use Pooled StDev = 2.05 ST hw7

4 4. Dodge claims that the gas mileage for a Durango is at least that of a Ford Explorer. A consumer wishes to test this claim and obtains a sample of gas mileages for 13 Durangos and 15 Explorers. Test the appropriate hypotheses at the.05 significance level. Assume that the sample is normally distributed. Two Sample T Test and CI: Durango, Explorer Two sample T for Durango vs Explorer N Mean StDev SE Mean Durango Explorer Difference = mu Durango mu Explorer Estimate for difference: % upper bound for difference: 0.33 T Test of difference = 0 (vs <): T Value =? P Value = DF = 26 Both use Pooled StDev = 2.65 Use the output above to answer the following: Pooled variance estimate: Degrees of Freedom: ST hw7

5 5. 60 athletes were selected to participate in a study to see if a particular training regimen was effective in increasing speed. Each individual was timed in the 40 yd dash before training began. After 3 months of the training program, 40 yd dash times were again recorded. The sample mean of the pre and post times are and sec respectively. The sample standard deviation of the differences is Was the program successful in increasing speed at the α =.05 LOS? Answer the following by hand: X d = Degrees of Freedom: ST hw7

6 Compute a (1 α)100% Confidence Interval for µ d : Homework 7 Check your answers above with the following Minitab Printout: Paired T Test and Confidence Interval Paired T for Pre_time Post_time N Mean StDev SE Mean Pre_time Post_tim Difference % CI for mean difference: ( , ) T Test of mean difference = 0 (vs > 0): T Value = P Value = ST hw7