Stats Material to Study (from wrong answers on practice tests)

Type of data: The average monthly temperature in degrees Fahrenheit for the city of Wilmington, Delaware,

throughout the year

Quantitative, Interval

Type of data: The ages of the respondents in a survey.

Quantitative, Ratio

Type of data: The years in which the respondents to a survey were born.

Quantitative, Interval

What do you say when you’re interpreting a z-score

the value __ is _ Standard Deviations above/below the mean

What do you say when you’re interpreting a coefficient of variation

the SD accounts for _% of the mean

Which numerical measure could you use to characterize the direction of the relationship between two

variables in the graph?

both the correlation coefficient and covariance

How do you compute a weighted mean

Multiply each value by its corresponding weight, then divide by the TOTAL number of days/etc.

An investor wants to know today’s average closing price of the stocks listed on the Standard and Poor’s 500

Index. Will the investor calculate a population parameter or sample statistic?

Population parameter

Does this require addition for the relative frequency or cumulative relative frequency: What percentage of the stocks in the Dow Jones Industrial Average received a sentiment rating less than 8?

Cumulative relative frequency

Does this require addition for the relative frequency or cumulative relative frequency: What percentage of the stocks in the Dow Jones Industrial Average received a sentiment rating of 6 or more?

Relative frequency

How do you calculate a relative frequency distribution based on the cumulative relative frequency distribution?

Go backward from CRF → relative frequency, you just take the difference between each pair of cumulative values.

How do you convert relative frequency to frequency?

multiply each relative frequency by n

T/F: the sampling distribution of the mean describes the pattern that individual observations tend to follow when randomly drawn from a population

F

T/F: If the population does not follow the normal probability distribution, the Central Limit Theorem tells us that the sample means will be normally distributed with sufficiently large sample size. In most cases, sample sizes of 5 or more will result in sample means being normally distributed, regardless of the shape of the population distribution

F

T/F: For any sample size n, the sampling distribution of 𝑥̅ is normal if the population from which the sample is drawn is uniformly distributed

F

Why is the Central Limit Theorem important for statistical analysis?

The value of the CLT is found in its conclusion that regardless of the shape of the population

distribution, sample means will form a normal distribution.

The number of hours spent studying by students on Michigan State campus in the week before final exams follows a normal distribution with standard deviation 9.5 hours. Two parallel studies take random samples of these students – one sample in each study. Assume that research team 1 uses a sample of 10 students, and research team 2 uses a random sample of 50 students. To sense if the results of two teams are comparable, they need to calculate the probability that the sample mean study hours are within 3 hours of the true population mean study hours. Without doing the calculations, state whether this probability will be higher for the first or the second research team.

This probability will be higher for the second team that uses a bigger sample size. The standard error of the mean will be smaller for the team 2 because of the larger sample size. As the standard error of the mean gets smaller, the sampling distribution becomes taller in the middle which also implies that the probability that a sample mean falls within an interval around the population mean increases.

With a proportion, what conditions must be met to use the normal distribution approximation

np>=5 and nq>=5

To analyze the mean and shape of the sampling distribution, what do we need to know

the population mean

What do we need to calculate the EXACT SE of the mean

the population SD

Why can you use the standard normal distribution to calculate the probability of the sample mean for any sample size

the sampling distribution of the sample mean is always normal, if the population is normal. if not, refer to CLT if n is large

T/F: The purpose of generating a confidence interval for the mean is to provide an estimate for the value of the population mean

T

T/F: The point estimate for the population mean will always be found within the limits of the confidence interval for the mean

T

T/F: Five random samples, each of size 40, are selected from a population of interest. A 90% confidence interval using a z-score is calculated for each sample. The margin of error for each confidence interval need not be the same

F

T/F: When the sample size is more than 30 and sigma is known, the population must be normally distributed to calculate a confidence interval

F

T/F: When the population standard deviation is unknown, we substitute the sample standard deviation in its place to calculate confidence intervals

T

T/F: The shape of the t-distribution becomes similar to the binomial distribution as the sample size increases

F

how would the confidence interval change (become wider/narrower) if the confidence level decreased

narrower

how would the confidence interval change (become wider/narrower) if the sample size decreased

wider

To construct the confidence interval, we want the sampling distribution of 𝑥̅ to be

normal

how do you interpret a confidence interval

We expect that x% of all possible sample averages for __ will produce confidence intervals that include the overall mean

how would the CI change (become wider/narrower) if the confidence level increased

wider

what is the point estimate of the population proportion

the sample proportion

for proportions, do we need any assumptions if the CI is desired

yes, that np>=5 and nq>=5

what do we need to know to calculate the SE of the sampling distribution of the sample proportion

the population proportion

Margin of Error formula

za/2 * SD/sqrt(n)

what formula do we use for the SE of the sampling distribution?

SE of the mean formula

the mean of the sampling distribution is always equal to

the population mean

when do we reject h0 in terms of p and test statistic

p‑value < α, zx>zα (r-tail), zx<−zα (l-tail), zx<−zα/2 or zx>zα/2 (2-tail)

when do we not reject h0 in terms of p and test statistic

p‑value ≥ α, z≤zα (r-tail), z≥−zα (l-tail), −zα/2 ≤ z ≤ zα/2 (2-tail)

How do you identify a right tail vs. left tail vs. 2-tail test

LOOK AT THE SYMBOL IN H1, right tailed= >, left tailed= <, 2-tailed= not equal

what symbols in the h0 and h1 are shown if the problem uses the term “different than”

= or =/ — not specific

how do you interpret the p-value for a right-tailed test

The p‑value is the probability of getting a test statistic greater than your observed value, assuming H0 is true.

how do you interpret the p-value for a left-tailed test

The p‑value is the probability of getting a test statistic less than your observed value, assuming H0 is true.

how do you interpret the p-value for a two-tailed test

The p‑value is the probability of getting a test statistic as far from 0 as yours, in either direction, assuming H0 is true.

when do you need additional assumptions about the population to conduct the hypothesis test

n<30, need to assume the population is normally distributed. if its a population proportion, we need to assume the np rules.

what do we compare when we are trying to state a conclusion for the HT given your critical value

we compare the critical value from the table, and the computed test statistic

When comparing 2 population means, what are the hyp statements for a right-tailed test

H0:μ1−μ2≤0

H1:μ1−μ2>0

When comparing 2 population means, what are the hyp statements for a two-tailed test

H0:μ1−μ2=0

H1:μ1−μ2≠0

When comparing 2 population means, what are the hyp statements for a left-tailed test

H0:μ1−μ2≥0

H1:μ1−μ2<0

only calculate a pooled variance when:

you are doing a test where both population SDs are unknown, OR you are told to assume equal variances