Null vs. Alternative Hypotheses
State the difference between Null and Alternative Hypotheses
Null: A statistical hypothesis that contains a statement of equality such as ≤, =, or ≥. Denoted H0 read “H subzero” or “H naught.”
Alternative: A statement of inequality such as >, ≠, or <. Must be true if H0 is false. Denoted Ha read “H sub-a.”
Define Hypothesis Test
A process that uses sample statistics to test a claim about the value of a population parameter.
Define to two types of errors
Type 1 error - rejecting H0 when it is true.
Type 2 error - failing to reject H0 when it is false.
For each claim, state H0 and Ha. Then determine whether the hypothesis test is a left-tailed, right-tailed, or two-tailed test. Sketch a normal sampling distribution and shade the area for the P-value.
A school publicizes that the proportion of its students who are involved in at least one extracurricular activity is 61%.
H0: p = 0.61
Ha: p ≠ 0.61
Two-tailed test
Define the Decision rule based on P-Value and Draw the chart.
See Chart
A school publicizes that the proportion of its students who are involved in at least one extracurricular activity is 61%.
H0 : p = 0.61 --> Equality Condition (Claim)
Ha : p ≠ 0.61 --> Compliment
Define Statistical Hypothesis
A statement, or claim, about a population parameter.
Draw the Types of Errors Chart
On the board
For each claim, state H0 and Ha. Then determine whether the hypothesis test is a left-tailed, right-tailed, or two-tailed test. Sketch a normal sampling distribution and shade the area for the P-value.
A car dealership announces that the mean time for an oil change is less than 15 minutes.
H0: μ ≥ 15 min
Ha: μ < 15 min
Left-tailed test
You perform a hypothesis test for the following claim. How should you interpret your decision if you reject H0? If you fail to reject H0?
H0 (Claim): A school publicizes that the proportion of its students who are involved in at least one extracurricular activity is 61%.
The claim is represented by H0.
If you reject H0 you should conclude “there is sufficient evidence to indicate that the school’s claim is false.”
If you fail to reject H0, you should conclude “there is insufficient evidence to indicate that the school’s claim (proportion of students who are involved in at least one extracurricular activity) is false.”
A car dealership announces that the mean time for an oil change is less than 15 minutes.
H0 : μ ≥ 15 minutes --> Compliment
Ha : μ < 15 minutes --> Inequality Condition (Claim)
Define Level of significance
Your maximum allowable probability of making a type I error. (Denoted by α, the lowercase Greek letter alpha.)
The USDA limit for salmonella contamination for chicken is 20%. A meat inspector reports that the chicken produced by a company exceeds the USDA limit. You perform a hypothesis test to determine whether the meat inspector’s claim is true. When will a type I or type II error occur? Which is more serious?
H0 : p ≤ 0.2
Ha : p > 0.2 (Claim)
A type I error is rejecting H0 when it is true. --> The actual proportion of contaminated chicken is less than or equal to 0.2, but you decide to reject H0.
A type II error is failing to reject H0 when it is false. --> The actual proportion of contaminated chicken is greater than 0.2, but you do not reject H0.
With a type II error, you could be allowing chicken that exceeded the USDA contamination limit to be sold to consumers. A type II error could result in sickness or even death.
For each claim, state H0 and Ha. Then determine whether the hypothesis test is a left-tailed, right-tailed, or two-tailed test. Sketch a normal sampling distribution and shade the area for the P-value.
A company advertises that the mean life of its furnaces is more than 18 years.
H0: μ ≤ 18 yr
Ha: μ > 18 yr
Right-tailed test
You perform a hypothesis test for the following claim. How should you interpret your decision if you reject H0? If you fail to reject H0?
Ha (Claim): A car dealership announces that the mean time for an oil change is less than 15 minutes.
The claim is represented by Ha.
H0 is “the mean time for an oil change is greater than or equal to 15 minutes.”
If you reject H0 you should conclude “there is enough evidence to support the dealership’s claim that the mean time for an oil change is less than 15 minutes.”
If you fail to reject H0, you should conclude “there is not enough evidence to support dealership’s claim that the mean time for an oil change is less than 15 minutes.”
A ketchup company regularly receives large shipments of tomatoes. For each shipment that is received, a supervisor takes a random sample of 500 tomatoes to see what percent of the sample is bruised and performs a significance test. If the sample shows convincing evidence that more than 10 percent of the entire shipment of tomatoes is bruised, then they will request a new shipment of tomatoes.
H0:p=0.1
Ha:p>0.1
Define P-value
The probability, if the null hypothesis is true, of obtaining a sample statistic with a value as extreme or more extreme than the one determined from the sample data.
A group of culinary arts students is comparing two methods for preparing asparagus: traditional steaming and a new frying method. They want to know if patrons of their school restaurant prefer their new frying method over the traditional steaming method. A sample of patrons are given asparagus prepared using each method and asked to select their preference. A statistical analysis is performed to determine if more than 50% of participants prefer the new frying method:
Type I error occurs if they reject the null hypothesis and conclude that their new frying method is preferred when in reality is it not. This may occur if, by random sampling error, they happen to get a sample that prefers the new frying method more than the overall population does. If this does occur, the consequence is that the students will have an incorrect belief that their new method of frying asparagus is superior to the traditional method of steaming.
Type II error occurs if they fail to reject the null hypothesis and conclude that their new method is not superior when in reality it is. If this does occur, the consequence is that the students will have an incorrect belief that their new method is not superior to the traditional method when in reality it is.
A restaurant owner installed a new automated drink machine. The machine is designed to dispense 530 mL, of liquid on the medium size setting. The owner suspects that the machine may be dispensing too much in medium drinks. They decide to take a sample of 30 medium drinks to see if the average amount is significantly greater than 530 mL
H0:μ=530 mL
Ha:μ>530 mL
Define the 3 types of hypothesis tests and draw and example of each
Left-Tailed, Right-Tailed, Two-Tailed