Hypothesis Test Rationale
Explain why we reject the null hypothesis if the p-value is less than the significance level.
Because our data is considered extreme if the null hypothesis is assumed.
Given the claim "The mean age of female students is less than that of male students," express this claim in symbolic form.
\mu_1 < mu_2
A researcher wants to know if the brand of smartphone (e.g., Apple, Samsung, Google) a person owns is independent of their primary news source (e.g., TV, Social Media, Print). What specific hypothesis test should be used?
Test for independence
A researcher computes a correlation coefficient of r = -0.92. Is this a
a) strong positive correlation
b) strong negative correlation
c) weak positive correlation
d) weak negative correlation
e) not a valid value for correlation
b) strong negative correlation
Why is it statistically incorrect to claim that we "accept" or "prove" the null hypothesis based on the results of a hypothesis test?
One sample is not enough to establish the validity of the null hypothesis, it is enough to disprove it, though.
A researcher is testing whether the mean age of students at a university is different from 22 years. Identify the null ( H_0 ) and alternative (H_1 ) hypotheses.
H_0: \mu = 22
H_1: \mu \ne 22
A botanist believes a new fertilizer will cause plants to grow to a mean height greater than 30 cm. She tests this on a sample of 25 plants, and she does not know the population standard deviation. What specific hypothesis test (from the list of 13) should she use?
One-sample test for mean with unknown population standard deviation.
A researcher finds a correlation of r = 0.15 between hours spent studying and scores on a final exam, with a sample size of n=150. Calculate the test statistic t and p-value for a test of significance for this correlation coefficient.
Test statistic:
t = 0.15/\sqrt((1-0.15^2)/(150-2)
p-value:
p = \text(2*T.DIST)(t,150-2)
What is the general form (as a fraction) for both z and t test statistics? What do the numerator and the denominator represent?
test statistic =
\text{sample statistics - population parameter}/\text{standard error}
If your confidence level is 98% and your calculated p-value is 0.034, what decision should you make regarding the null hypothesis?
FTR
A sociologist wants to determine if the distribution of political affiliations (Democrat, Republican, Independent, Other) in a specific county matches the known statewide distribution. She surveys 500 residents of the county.
Goodness of Fit
Why is it important to look at the scatter plot of the data before conducting a test for correlation?
You can get a small p-value even though the data is not linearly correlated.
Why do I multiply NORM.DIST by 2 when finding the p-value of a two-tailed test for a one-sample test for proportion.
We want to include the area of the tail on the other side of the bell curve.
You are conducting a two-tailed test, and your test statistic is z=1.9 . What is the p-value? Give me the Excel formula.
= 2*NORM.S.DIST(-1.9)
OR
=2*(1-NORM.S.DIST(1.9))
A pharmaceutical company wants to test the effectiveness of a new weight-loss drug. They measure the weight of 50 participants before they start the drug and then measure their weight again after 12 weeks on the drug. They want to know if there is a significant mean difference in weight.
Matched Pairs
My original claim is that there is a correlation between shark attacks and ice cream consumption. I get a p-value of 0.32. What is my step 8?
There is not enough evidence (p=0.320) to suggest that there is a correlation between shark attacks and ice cream consumption, with 95% confidence.
What is the rationale behind failing to reject the null hypothesis when the p-value is not lower than alpha .
My data is not considered extreme, according to the null hypothesis, so the null hypothesis is OK.
You find a sample correlation coefficient of r = 0.30 from a sample of n=50. What is the value of the test statistic t used for a test of significance for a correlation coefficient?
t = .30 /sqrt((1-(.30)^2)/(50-2)
A consumer advocacy group wants to compare the mean battery life of two different brands of smartphones (Brand A and Brand B). They test 30 phones from each brand. They know the population standard deviations for the battery life of both brands, and these standard deviations are not equal.
Two-sample test for the mean with known, unequal population standard deviation.
What happens to the correlation coefficient if I multiply every value in one of the datasets by 3?
r is unchanged