Chapter 8 Hypothesis Test Significance Tests Means Part

+ Chapter 8: Hypothesis Test Significance Tests: Means Part 2

One Potato, Two Potato Tests About a Population Proportion A potato-chip producer has just received a truckload of potatoes from its main supplier. If the producer determines that more than 8% of the potatoes in the shipment have blemishes, the truck will be sent away to get another load from the supplier. A supervisor selects a random sample of 500 potatoes from the truck. An inspection reveals that 47 of the potatoes have blemishes. Carry out a significance test at the α = 0. 10 significance level. What should the producer conclude? + n Warmup:

One Potato, Two Potato + n Warmup: p is the true proportion of potatoes in this shipment with blemishes. H 0: p = 0. 08 Ha: p > 0. 08. The sample proportion of blemished potatoes is P-value = 0. 1251 Tests About a Population Proportion A potato-chip producer has just received a truckload of potatoes from its main supplier. If the producer determines that more than 8% of the potatoes in the shipment have blemishes, the truck will be sent away to get another load from the supplier. A supervisor selects a random sample of 500 potatoes from the truck. An inspection reveals that 47 of the potatoes have blemishes. Carry out a significance test at the α = 0. 10 significance level. What should the producer conclude? we fail to reject H 0 There is not enough evidence to say that the shipment contains more than 8% blemished potatoes. The producer will use this truckload of potatoes to make potato chips.

Formulas Significance Tests: The Basics Use for Proportions + n The

Formulas Use for Means when the Population Standard Deviation is known Significance Tests: The Basics Use for Proportions + n The

Formulas Use for Means when the Population Standard Deviation is known Use for Means when the sample Standard Deviation is known Significance Tests: The Basics Use for Proportions + n The

Formulas Use for Means when the Population Standard Deviation is known Use for Means when the sample Standard Deviation is known Df =n - 1 1 Prop z Test t Test Significance Tests: The Basics Use for Proportions + n The

Hypotheses + n Stating 1. State what the p or represents 2. State the Ho (always = ) 3. State the Ha (either ≠, <, or > ) Significance Tests: The Basics Remember that there are 3 parts to the hypotheses.

Calculator Key Strokes + n Example: Significance Tests: Means

Calculator Key Strokes Significance Tests: Means μ = The mean body temperature of all healthy adults H 0 : μ = 98. 6 Ha: μ < 98. 6 + n Example:

Calculator Key Strokes Significance Tests: Means μ = The true mean body temperature of all healthy adults H 0 : μ = 98. 6 Ha: μ < 98. 6 + n Example:

Calculator Key Strokes + n Example: Significance Tests: Means

Calculator Key Strokes t = -7. 12 P-value = basically zero reject the null hypothesis There very strong evidence to say that the true body temp of healthy adults is less than 98. 6. Significance Tests: Means μ = The mean body temperature of all healthy adults H 0 : μ = 98. 6 Ha: μ < 98. 6 + n Example:

Out a Significance Test for µ µ = the true mean lifetime of the new deluxe AAA batteries H 0: µ = 30 hours Ha: µ > 30 hours The p value is. 0728 Tests About a Population Mean A company claimed to have developed a new AAA battery that lasts longer than its regular AAA batteries. Based on years of experience, the company knows that its regular AAA batteries last for 30 hours of continuous use, on average. An SRS of 15 new batteries lasted an average of 33. 9 hours with a standard deviation of 9. 8 hours. Do these data give convincing evidence that the new batteries last longer on average? To find out, we must perform a significance test at a significance level of. 01. + n Carrying Because the P-value exceeds our α = 0. 01 significance level, We fail to reject the null hypothesis There is not enough evidence to say that the company’s new AAA batteries last longer than 30 hours.

Calculator Key Strokes Significance Tests: Means A researcher designs an experiment where a random sample of n = 50 high school seniors are given a pill to improve their concentration and problem solving skills. After being administered the pill, subjects take the SAT, and their scores on the SAT Math section are tabulated. The average score of student who took the pill is x = 540. Given that the average score of all high school seniors on the SAT Math is μ = 510 with standard deviation σ = 100, is there statistically significant evidence that students who took the pill scored higher? Use significance level of. 05. + n Example:

Calculator Key Strokes µ = the true mean SAT Score for students who took the pill. H 0 : µ = 510 hours Ha : µ >510 hours Significance Tests: Means A researcher designs an experiment where a random sample of n = 50 high school seniors are given a pill to improve their concentration and problem solving skills. After being administered the pill, subjects take the SAT, and their scores on the SAT Math section are tabulated. The average score of student who took the pill is x = 540. Given that the average score of all high school seniors on the SAT Math is μ = 510 with standard deviation σ = 100, is there statistically significant evidence that students who took the pill scored higher? Use significance level of. 05. + n Example:

Calculator Key Strokes µ = the true mean SAT Score for students who took the pill. H 0 : µ = 510 hours Ha : µ >510 hours Significance Tests: Means A researcher designs an experiment where a random sample of n = 50 high school seniors are given a pill to improve their concentration and problem solving skills. After being administered the pill, subjects take the SAT, and their scores on the SAT Math section are tabulated. The average score of student who took the pill is x = 540. Given that the average score of all high school seniors on the SAT Math is μ = 510 with standard deviation σ = 100, is there statistically significant evidence that students who took the pill scored higher? Use significance level of. 05. + n Example:

Calculator Key Strokes Significance Tests: Means A researcher designs an experiment where a random sample of n = 50 high school seniors are given a pill to improve their concentration and problem solving skills. After being administered the pill, subjects take the SAT, and their scores on the SAT Math section are tabulated. The average score of student who took the pill is x = 540. Given that the average score of all high school seniors on the SAT Math is μ = 510 with standard deviation σ = 100, is there statistically significant evidence that students who took the pill scored higher? Use significance level of. 05. + n Example:

Calculator Key Strokes µ = the true mean SAT Score for students who took the pill. H 0 : µ = 510 hours Ha : µ >510 hours z = 2. 12 P value =. 0169 Significance Tests: Means A researcher designs an experiment where a random sample of n = 50 high school seniors are given a pill to improve their concentration and problem solving skills. After being administered the pill, subjects take the SAT, and their scores on the SAT Math section are tabulated. The average score of student who took the pill is x = 540. Given that the average score of all high school seniors on the SAT Math is μ = 510 with standard deviation σ = 100, is there statistically significant evidence that students who took the pill scored higher? Use significance level of. 05. + n Example:

Calculator Key Strokes + n Example: z = 2. 12 reject Ho P value =. 0169 Significance Tests: Means µ = the true mean SAT Score for students who took the pill. H 0 : µ = 510 hours Ha : µ >510 hours

Calculator Key Strokes µ = the true mean SAT Score for students who took the pill. H 0 : µ = 510 hours Ha : µ >510 hours z = 2. 12 reject Ho strong evidence that the SAT Score for those who took the pill is higher than 510 P value =. 0169 Significance Tests: Means A researcher designs an experiment where a random sample of n = 50 high school seniors are given a pill to improve their concentration and problem solving skills. After being administered the pill, subjects take the SAT, and their scores on the SAT Math section are tabulated. The average score of student who took the pill is x = 540. Given that the average score of all high school seniors on the SAT Math is μ = 510 with standard deviation σ = 100, is there statistically significant evidence that students who took the pill scored higher? + n Example:

IQ Significance Tests: Means A principal at a certain school claims that the students in his school are above average intelligence. A random sample of thirty students IQ scores have a mean score of 112. Is there sufficient evidence to support the principal’s claim? The mean population IQ is 100 with a standard deviation of 15. Use a significance level of 5%. + n Example:

IQ µ = the true mean IQ of the students in his school. H 0 : µ = 100 hours Ha : µ > 100 hours Significance Tests: Means A principal at a certain school claims that the students in his school are above average intelligence. A random sample of thirty students IQ scores have a mean score of 112. Is there sufficient evidence to support the principal’s claim? The mean population IQ is 100 with a standard deviation of 15. Use a significance level of 5%. + n Example:

IQ µ = the true mean IQ of the students in his school. H 0 : µ = 100 hours Ha : µ > 100 hours Significance Tests: Means A principal at a certain school claims that the students in his school are above average intelligence. A random sample of thirty students IQ scores have a mean score of 112. Is there sufficient evidence to support the principal’s claim? The mean population IQ is 100 with a standard deviation of 15. Use a significance level of 5%. + n Example:

IQ µ = the true mean IQ of the students in his school. H 0 : µ = 100 hours Ha : µ > 100 hours z = 4. 38 Significance Tests: Means A principal at a certain school claims that the students in his school are above average intelligence. A random sample of thirty students IQ scores have a mean score of 112. Is there sufficient evidence to support the principal’s claim? The mean population IQ is 100 with a standard deviation of 15. Use a significance level of 5%. + n Example:

IQ µ = the true mean IQ of the students in his school. H 0 : µ = 100 hours Ha : µ > 100 hours z = 4. 38 P value =. 00000589 Significance Tests: Means A principal at a certain school claims that the students in his school are above average intelligence. A random sample of thirty students IQ scores have a mean score of 112. Is there sufficient evidence to support the principal’s claim? The mean population IQ is 100 with a standard deviation of 15. Use a significance level of 5%. + n Example:

IQ µ = the true mean IQ of the students in his school. H 0 : µ = 100 hours Ha : µ > 100 hours z = 4. 38 P value =. 00000589 reject Ho Very strong evidence that the true IQ score for this school is higher than 100. Significance Tests: Means A principal at a certain school claims that the students in his school are above average intelligence. A random sample of thirty students IQ scores have a mean score of 112. Is there sufficient evidence to support the principal’s claim? The mean population IQ is 100 with a standard deviation of 15. Use a significance level of 5%. + n Example: