Stats Unit 4 Exam

How would you find a 95% confidence interval for the population proortion who (category of interest)?

1. Identify population, sample, parameter, statistic 2. Check the 3 conditions are met 3. Plug numbers into p hat +/- 1.96x [square root of (p hat(1-phat)/n)] -this will give you the 95% range, or confidence interval, for the problem

Describe the conclusion step?

1. If you rejected H0: There is significant evidence that the population proportion of... that (thing of interest) is more/less than p0 value 2. If you fail to reject H0: There is not significant evidence that the population proportion of... that (thing of interest) is more/less than p0 value

What are the three assumptions that need to be met in order for the shape to follow the normal model?

1. Random sample 2. Success/Failure condition (S/F) np ≥ 10 and n(1 - p) ≥ 10 -have to have both of these pass 3. 10% Condition n must be less than 10% of population

Describe the assumptions and coniditons step?

1. Random sample condition 2. Success/failure condition np0 ≥ 10 n(1-p0) ≥ 10 3. 10% condition

What is the decision step?

1. Reject the null hypothesis -when p value is smaller than alpha value 2. Do not reject the null hypothesis -when p value is greater than alpha value

How do you learn about long term behavior of random samples and the sample proportion (p hat)?

1. Take sample from population 2. Obtain information on categorical variable 3. Calculate sample proportion of category of interest 4. Repeat Steps 1 through 3 many times

What is the hypothesis test procedure?

1.Null Hypothesis 2.Alternative Hypothesis 3.Assumptions 4.Sampling Distribution if Null Hypothesis is True 5.Test Statistic 6.P-value 7.Decision 8.Conclusion

How do you calculate the width of confidence intervals?

2 X margin of error

What are the z* values for 80%, 90%, 95%, 98%, and 99%?

80%: 1.282 90%: 1.645 95%: 1.96 98%: 2.326 99%: 2.576

Categorical Variable

A variable with labels as values (categories) Typically interested in one specific category

How would you answer questions like: What percent of all samples of size 250 will have a sample proportion of left-handed people greater than 13.5%? What is the probability of getting a sample proportion of left-handed people less than 6% in a sample of 250 people?

Calculate a z score with this equation z= (p hat-p)/standard deviation

What happens to the standard deviation as you increase sample size? The bigger the sample....

Decreases The closer we expect our sample value to be to the true proportion

Sampling Distribution of Sample Proportion? How can you see this graphically?

Distribution of all possible values of the sample proportion that can occur in repeated sampling from population -Make a histogram of the repeated trials

How can you apply the 68-95-99.7% Rule to sampling distribution of a proportion? What does this allow us to calculate?

Each percent is allocated with a specific number For example, 95% is 1.96 so the equation is... In 95% of all samples, the sample proportion p hat will be between the two values (p-1.96 x standard deviation) and (p+1.96 x standard deviation) This means that in 95% of all samples, the sample proportion p hat will be within 1.96 standard deviations of the population proportion p. p is within 1.96 x standard deviation of p hat If we have a p hat, then we can come up with the distance p hat is from p or find the chance p hat is within a certain distance of p

What is the meaning of 'confidence'

For a single sample - we don't know if the population proportion is in the interval or not, but we can be C% confident.

Population

Group of people you want to collect information from Information = Categorical Variable with one category of interest

What is the sampling distribution step?

If p=p0 then p hat is N(p0, [square root of (p0(1-p0)/n)]) N(mean, standard deviation)

How do you calculate standard deviation when you don't know p? What is this called?

Plug in p hat into the formula instead p is within ... [square root of (p hat(1-phat)/n)] Confidence intervals

What are the three things to look at in a sampling distribution histogram?

Shape Normal or not Center (mean) What value is the distribution of the sample proportion values centered at? Did this value stay the same? Spread (standard deviation) What is the standard deviation of the distribution of the sample proportion values? Increase or decrease with more random samples?

Sample

Smaller group selected from population that we obtain information from Information = Categorical Variable with one category of interest

What is the equation for standard deviation? How can we write the sampling distribution for a sample proportion, if it follows a normal model?

Square root of [(p(1-p))/n] N (mean, standard deviation)

Statistic?Symbol? How would you describe this?

Statistic = summary of information collected from sample p hat = proportion of sample members in category of interest Proportion of (sample) in sample size of... who (category of interest)

What happens to shape and center when increasing the sample size?

Stay the same

Population distribution? Sample distribution?

The distribution of the categorical variable of interest in the population The distribution of the categorical variable of interest in the sample

What is the p-value step?

The p value is the probability of getting a value for the test statistic more extreme if the null hypothesis is true Use the z table to find this proportion If p<p0 the p value = proportion from z table If p>p0 the p value = 1 - z table proportion If p doesnt equal p0 the p value = 2(1 - z table proportion)

Describe alternative hypothesis step?

This is the claim about the parameter that you would like to find evidence for Have three options to choose from 1. p<p0 2. p>p0 3. p doesnt equal p0

Describe the null hypothesis step?

This is what the parameter is assumed to be -Based on past information or on previously held belief -the value for the specific example symbol is p0

sampling Variability?

This means the sample statistics vary from sample to sample

How do you interpret a confidence interval?

We are ...% confident the parameter who (category of interest) is between (confidence interval)

What is the test statistic step?

calculate the z value z= (p hat - p0)/ [square root of (p0(1-p0)/n)]

What is hypothesis testing? How would you apply this to a proportion?

method of analyzing data to draw a conclusion about a "hypothesized" value for a population parameter. 1. We have a claim about a population proportion 2. We want to test if the claim is true 3. Obtain data 4. Test the claim -Make use of sampling distributions -Use the normal distribution to calculate a p-value -Determine if there is evidence to support our claim based on the data (using the p-value)

How do yu calculate the margin of error without knowing the p hat value?Sample size calculation formula? which way do you round a number?

plug in .5 instead and solve for n n _> (.5z*/ME)^2 up

Parameter? Symbol? Is it known or unknown? How do you describe this?

summary of information wanted from population p = proportion of population members in category of interest The true proportion is usually unknown to us. Proportion of all... (population group) who... (category of interest)

How do you calculate the margin of error? How does the size of the confidence level effect the ME? How does sample size affect ME size?

z* x [square root of (p hat(1-phat)/n)] always a percent Smaller confidence level means smaller ME, smaller width Larger confidence level means larger ME, larger width To have more confidence in your interval, the interval must be wider Smaller samples mean larger ME Larger samples mean smaller ME Idea: Larger samples give more precise estimates of the population proportion.