HW10 Skeleton

10.1

• 1. Hypothesis
• 2. Hypothesis Testing
• 3. Null Hypothesis
• 4. Alternative Hypothesis
• 5. Type I Error
• 6. Type II Error
• 7. Level of Significance
• 8. False. Without having access to the entire population sameple evidence cannot prove that a null hypothesis is true.
• 9. The hypothesis test is right-tailed. The parameter being tested is population mean μ.
• 10. The hypotheis test is left-tailed. The parameter being tested is population proportion
• 11. The hypotheis test is two-tailed. The paramter being tested is population standard deviation “σ”.

18. 1. Ho (null hypothesis): μ = 32 ounces H1 (alternative hypothesis): μ < 32 ounces

    2. Making a Type I Error would mean concluding that the consumer advocate rejects the hypothesis that the mean content is 32 ounces when, in fact, the mean content is actually 32 ounces.

    3. Making a Type II error would mean concluding that the consumer advocate fails to reject the hypothesis that the means content is 32 ounces when in the fact the mean contect is actually less than 32 ounces.

19. 1. Ho (null hypothesis): σ = 0.7 psi H1 (alternative hypothesis): σ < 0.7 psi.

    2. Making a Type I error would mean concluding that the pressure variability had been reduced below 0.7 psi when, in fact, the pressure variability had not been reduced below 0.7 psi.

    3. Making a Type II error would mean concluding that the pressure variability has not been reduced below 0.7 psi, when in fact the pressure variability had been reduced below 0.7 psi.

 

36. 1. The null hypothesis is the that the mean consumption of popcorn annually by Americans is 54 quarts. Ho (null hypothesis): μ = 54 The alternative hypothesis is that the mean consumption of popcorn annually by Americans is greater than 54 quarts after the marketing campaign. H1 (alternative hypothesis): μ > 54

    2. After an aggressivve marketing campaign there is enough evidence to reject the null hypothesis. Therefore, we can conclude that the mean consumption of popcorn annually by Americans is greater than 54 quarts–the previous mean consumption.

    3. If the mean annual consumption was actually 53.4 quarts after the marketing campaign this would be a Type I error because we rejected the null when it was in fact true. If this was tested at a α=0.05 level then there would be a 0.05 probability of committing a Type I error.

37. 1. To test the hypothesis is that the proportion of high schools students currently using e-cigs is higher than 2.8% at the counselor’s high school. Ho (null hypothesis): p = 0.0280 altnernative hypothesis: p > 0.0280

    2. There is not sufficient evidence to conclude that more than 2.8% of the students at the counselor’s school use e-cigs.

    3. Type II error, because the null hypothesis was not rejected when, in fact, the alternative hypothesis was true.