Stats final exam

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Conditions for 1-sample t for means

1. Randomness of data collection 2. Normality of population (plot has no outliers) or large sample size

conditions for matched pairs t for mean of differences

1. Randomness of data collection 2. Normality of population (plot has no outliers) or large sample size (applied to differences)

Conditions for chi-square

1. Randomness of data collection 2. Large sample size (All expected counts > 5)

Conditions for 2 sample z for proportions

1. Randomness of data collection 2. Normality of the sampling distribution of 𝑝𝑝̂ 1 − 𝑝𝑝̂ 2:

Conditions for 1-sample z for proportions

1. Randomness of data collection 2. Normality of the sampling distribution of 𝑝𝑝̂:

Conditions for 2-sample t for difference of means (pooled variance)

1. Randomness of data collection 2.Normality of populations (sample plots have no outliers) or large n 3. Equal population standard deviations (Largest s/smallest s < 2)

Conditions for ANOVA

1. Randomness of data collection 2.Normality of populations (sample plots have no outliers) or large n 3. Equal population standard deviations (Largest s/smallest s < 2)

Suppose you want to estimate the proportion of voters who will vote for George Smith, a candidate for state representative. How many should you sample in order to estimate ​p​ with a margin of error of 0.05 (5%) and 95% confidence?

385

Role type classification for Chi-Square

C -> C

Role type classification for 2-sample z for proportions

C -> C Explanatory variable has 2 levels

Role type classification for ANOVA (Analysis of Variance)

C -> Q Explanatory variable has 3+ levels

Role type classification for 2-sample t for difference of means (pooled variance)

C -> Q Explanatory variable has two levels

Role type classification for Matched pairs t for mean of differences

C -> Q Explanatory variable has two levels

Role type classification for 1-sample z for proportions

Categorical

Hypothesis for 1-sample t for means

H0: µ = µ0 Ha: µ > µ0 µ < µ0 µ ≠ µ0

Hypothesis for Chi-Square

Ho: There is no association Ha: There is an association

Hypothesis for Linear Regression

Ho: There is no linear relationship between the two variables Ha: There is a linear relationship between the two variables

Hypothesis for 1-sample z for proportions

Ho: p = po Ha: p > po p < po p ≠ po

Hypothesis for 2-sample z for proportions

Ho: p1 = p2 Ha: p1 < p2 p1 > p2 p1 ≠ p2

Hypothesis for 2-sample t for difference of means (pooled variance)

Ho: µ1 = µ2 Ha: µ1 > µ2 µ1 < µ2 µ1 ≠ µ2

Hypothesis for ANOVA (Analysis of Variance)

Ho: µ1 = µ2 = ... = µn Ha: at least one mean is different

hypothesis for Matched pairs t for mean of differences

Ho: 𝜇𝑑 = 0 Ha: 𝜇𝑑 > 0 𝜇𝑑 < 0 𝜇𝑑 ≠ 0

conditions for linear regression

Linearity- linear pattern in scatterplot Independence randomness in data collection Normality- (histogram of residuals is normal) Equal Pop. Stan. Dev. - scatterplot has no megaphone pattern

table to use for 2-sample z for proportions

P-value: z t for z*

table used for 1-sample z for proportions

P-value: z t for z*

Role type classification for Linear Regression

Q -> Q

To do regression inference, the data must satisfy all of the following ​except The response variable (y) has a Normal distribution at each value of x. The values of the explanatory variable (x) must follow a Normal distribution. The true relationship must be linear. The standard deviation of the y's about the true line is the same everywhere.

The values of the explanatory variable (x) must follow a Normal distribution.

df and table for chi-square

df = (r - 1) * (c - 1) r = num. of rows c = num. of columns table: chi-square

df and table for 1-sample t for means

df: n - 1 table: t

df and table for matched pairs t for mean of differences

df: n - 1 table: t

df and table for 2-sample t for difference of means (pooled variance)

df: n1 + n2 - 2 table: t

Changing the unit of measurement in the X or Y variable changes the value of r.

false

Margin of error for an approximate confidence interval for p is z* x square root of p(1-p) / n

false

The mean of the sampling distribution of the sample proportion equals p̂ .

false

We check np̂ ≥10 and n(1-p̂) ≥10 before obtaining the p-value to test H0: p = 0.60.

false

df for linear regression

n - 2

Which one of the following represents the parameter estimated with a 99% confidence interval for difference in proportions?

p1 − p2

Role type classification for 1-sample t for means

quantitative

Correlation ignores the distinction between explanatory and response variables.

true

Correlation is a valid measure of strength of relationship whenever the relationship between two different quantitative measurements on each individual appears linear in the scatterplot

true

We compute the standard error of p̂ using the formula square root of p(1-p) / n

true

When no information is available about the value of p and we need to determine sample size needed to estimate proportion, we can safely use p* = 0.5 in the sample size formula

true

μ1 − μ2 , the difference in two population means, represents the parameter used to compare the means of two populations.

true

What is the symbol for the difference between two population means?

μ 1 −μ2


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