Stats Chapter 10

A scientist has a null hypothesis Ho: μ = 60 and an alternate hypothesis Ha: μ not equal to 60. What kind of test is the scientist running?

For the not equal to case, the test is two-sided.

Which of the following are synonyms?

Paired data; matched samples

What can we NOT do with a null hypothesis?

Prove it to be true.

The variability of individual observations around their mean is known as the:

Standard deviation

Which of the following p-values indicates that the findings of the experiment are statistically significant?

The accepted p-value here is anything less then 0.05.

Which of the following types of data are required in order to run a chi-square?

The chi-square test looks at categorical data.

Null hypothesis

The hypothesis proposing that the independent variable will have no effect on the dependent variable

The t-value is supposed to be _____.

The last step is to check the t-value table and determine whether our calculated value exceeds the table value.

Which of the following is NOT an appropriate significance level for a study?

The significance level of a study should be set at 0.01, 0.05, or 0.10.

If the sample size is small and the population standard deviation is not known, we typically use the _____

The t-distribution is used for small sample sizes when the population standard deviation is not known.

How many hypotheses do you write in a hypothesis test?

You actually have two hypotheses to write.

Which of these best represents the null hypothesis?

p 1 is equal to p 2

p hat is a symbol used to represent which of the following?

p hat is the sample proportion that we use to estimate the population proportion, which is simply p.

How many types of errors can be made when interpreting statistical results?

two

In the z-test formula, what does n stand for?

Sample size.

In which of these disciplines can an ANOVA be used?

Social science, medical science, political science

Which of the following represents the probability of making a type II error?

The probability of making a type II error is labeled with a beta symbol that looks similar to the letter 'B'.

F-Ratio

Brian wants to know if there is a significant difference between the means in the study he is conducting. What value does Brian need to examine?

Between which of the following data does a chi-square measure the difference?

Collected and expected

For your hypothesis, you believe that many people own dogs. What kind of effect size would tell you that?

Large effect size

What does H_0 represent?

Null hypothesis

A scientist is testing the growth speeds of a species of algae, and makes the following null hypothesis: Specimens of this species grow at a rate of at least v. They set their region of acceptance at 95% or higher, and find that 93% of the specimens grow at a rate of at least v. What should the scientist do and why?

They should reject the null hypothesis, because their results are outside of the region of acceptance.

The purpose of running an ANOVA is to find the _____ .

differences between means

n is a symbol commonly used to denote which of the following?

sample size

Brian plans to have one group participate in different lengths of meditation time for his study to determine whether meditation affects body weight. After each length of meditation time, he will measure the body weight of each individual in the group. Brian's assistant, Barney, is worried that they will not see a big difference in the body weight of the participants from the first post-meditation weigh-in to the subsequent weigh-ins. What phenomenon is Barney worried about?

Carryover effect

Which of the following is TRUE about effect size in hypothesis testing?

Effect size is an objective and standardized measurement.

When calculating the t statistic, Kris is confused. For x-bar, he should put the mean of _____, and for mu, he should put the mean of _____.

His study; the population

Julie has done a study and her t statistic is smaller than the number in the t-table. This means that Julie should:

If a t-statistic is smaller than the number on the t-table, the null hypothesis is accepted. If it is larger, the null hypothesis is rejected.

In the equation for the test statistic of matched pairs, sd stands for the:

Standard deviation

The variability of the sample mean across different samples is called the:

Standard error is the variability of the sample meal across different samples.

What does n stand for in hypothesis testing?

The total number of paired sample differences

Some high school students were divided into two groups, group A and group B, and given the same test. Group A consisted of 6 students and the average score was 12 with a standard deviation of 2. Group B consisted of 8 students and the average score was 11 with a standard deviation of 3. The variability within the groups is:

For each group, square the standard deviation and then divide this by the number of students in each group. Add the results from both groups together. (2^2)/6 + (3^2)/8 = 0.667 + 1.125 = 1.792 Then, take the square root of this number to calculate the within group variability. Sqrt(1.792) = 1.339

What does the effect size tell us?

How much of an impact our effect has on our test population

Which of the following represents the probability of making a type I error?

In statistics, we label the probability of making a type I error with the alpha symbol that looks like an 'a'.

When are degrees of freedom lost?

In the process of calculating the standard deviation, two degrees of freedom are lost.

Identify the statement that appropriately describes the null hypothesis:

A null hypothesis is typically the standard assumption and is defined as the prediction that there is no interaction between the variables.

What does ANOVA stand for?

Analysis of variance

Why are proportions useful?

Because they allow us to look at a smaller sample of a population and determine what the larger population is likely to do.

The chi-square formula cannot function if the number of observed or expected is below which of the following?

The number of observed or expected cannot be less than five. This is too low of a number for the statistics to handle and basically results in invalid findings.

What are the two hypotheses that must be created when performing hypothesis testing for a proportion?

Null and alternate.

If the region of acceptance for a certain hypothesis is from 0% to 5%, then which of the following results is within the region of acceptance?

The region of acceptance is a chosen range of values that results in the null hypothesis being stated as valid. So if the region of acceptance is 0% to 5%, we know that 1% is a result that falls in this range. The other percentages are too great - they do not fall in the range.

What is the first step in a hypothesis test?

Writing the hypothesis

A recent study shows that in 25 out of 50 national parks, there was at least one drowning in the last ten years, while in 275 out of 500 state parks, there was at least one drowning in the last ten years. Using a significance level of 0.05, is there any difference in the proportion of national and state parks with at least one drowning in the last ten years, and what are the relevant z-scores?

There is no difference; -1.96 < -0.68 < 1.96

Which of the following is an example of a question that may be answered using hypothesis testing for a proportion?

One of the conditions for using a hypothesis for a proportion is that the answer choices have to be mutually exclusive. Only the question about married women meets that condition as the answer is either yes or no.

A scientist publishes a paper where they assert that their null hypothesis about the speeds required for clouds to form is false. They later find that clouds actually form much more quickly than they'd described in the paper, closer to the speeds described in the null hypothesis. What sort of error did the scientist make, and why?

We know that the scientist's research indicated that the speeds clouds form was actually closer to the speeds he described in the null hypothesis, even though he declared that to be false. With this in mind we know the scientist made a a type I error which happens when you say that the null hypothesis is false when it actually is true.

How many steps are there in hypothesis testing?

4

Khan is designing a study and needs to operationalize his variables. Which of the following variables is already operationalized?

Height in inches

What is a hypothesis?

An assumption about something.

When is a type II error made?

When your findings show that the null hypothesis is true when it actually is false.

What does H_A represent?

Alternative hypothesis

If the p-value is less than the significance α, we will _____.

We reject the null hypothesis if the p-value is less than the significance α.

Brian is conducting a study to determine whether meditation affects body weight. Brian plans to have three different groups, where each group will be assigned a different length of meditation time. When Brian gathers his data, he will compare the body weights of the participants between groups. Which type of ANOVA is Brian using?

Between subject

You are observing a psychologist run a chi-square. You see the psychologist take his number of categories and subtract 1. Which of the following is the psychologist calculating?

Degrees of freedom

Which of these is an example of paired data?

Explanation 'Five people being tested for the efficacy of a drug before and after treatment' is the correct answer because the source is the SAME. The same five people are tested before and after treatment. In the other examples, data is being used from different sources.

A researcher is interested in the cognitive performance of teenagers, and collects data from students from two different schools. For each student at the first school, the researcher compares the results against a student at the second school. Is the researcher using matched samples? Why or why not?

If both corresponding data values come from the SAME source, the samples are considered to be matched. In the example above, the data values came from two different schools. Because the data values are from DIFFERENT sources, they are not considered to be matched.

If the value of the mean μ as stated in the null hypothesis Ho is within the confidence interval, we _____.

If the population mean μ as expressed in the null hypothesis Ho is within the confidence interval, we fail to reject the null hypothesis.

Sherri is doing a study. She believes that the subjects in her study will do about the same as the entire population would. Thus, the belief that Sherri's mean does not differ from the population's mean is the _____ hypothesis, and the belief that Sherri's mean is significantly different from the population's mean is the _____ hypothesis.

Null; alternative

Alternative hypothesis

What is the hypothesis stating that there will be a difference between groups as indicated by the ANOVA performed on the data that is collected?

In order to conduct a study to determine whether meditation affects body weight, Brian plans to have one group participate in different lengths of meditation time. After each length of meditation time, Brian will measure the body weight of each individual in the group, which is _____ form of ANOVA.

In this situation, Brian is using a repeated measure ANOVA which indicates that the study uses the same group of participants for each level of the variable. Looking at this example, Brian will check in with the group after each meditation time. This gives him the same number of scores, but he will be repeating the measures instead of comparing between them.

A group of seven people have taken a quiz and their scores are 8,9,10,5,8,9 and 10. Calculate the standard deviation.

The mean score is (8+9+10+5+8+9+10)/7 = 8.4 Calculate the distance of each score from the mean and square the result, and add the result for all the scores together. 0.4^2+0.6^2+1.6^2+3.4^2+0.4^2+0.6^2+1.6^2 = 0.16+0.36+2.56+11.56+0.16+0.36+2.56 =17.72 Divide by 7 gives 17.72/7 = 2.53 Therefore, the population standard deviation is sqrt(2.53) = 1.6

Which of these is NOT a condition for using hypothesis testing for a proportion?

There are four conditions that must be met in order to use hypothesis testing for a proportion: random sampling, mutually exclusive outcomes, 10 successes and 10 failures, and population size at least 20 times as large as the sample size.

Kelly lives in Newark and commutes to New York City. She notices that the price of coffee seems to be different in the two cities. She buys 39 coffees in Newark and finds that they have an average price of $1.50, with a standard deviation of 25 cents. She buys 41 coffees in New York City and finds that they have an average price of $2.25, with a standard deviation of 50 cents. At a significance level of 0.05, is there a significant difference between the prices of coffee in the two cities? What are the relevant z-scores that lead you to your conclusion?

To solve this problem, use the equation for the z-test given in the lesson. z = (x1 - x2) - (u1 - u2) / √((standard deviation of set 1^2/n1) + (standard deviation of set 2^2/n2)) Plug the numbers into the formula to solve. You'll see that z equals 8.55, which is greater than 1.96, which means we reject the null hypothesis at the significance level of 0.05.

You are testing five different kinds of dog food to see which one gives dogs the most energy. Dog food 1 has an effect size of 0. Dog food 2 has a small effect size. Dog food 3 has a large effect size. Dog food 4 has a medium effect size. Dog food 5 has a small effect size. Which dog food performs the best?

We can compare the effect sizes of the different hypothesis tests to see which hypothesis test gives us the greatest effect size or the least effect size. Clearly, dog food 3 performed the best because it has the largest effect size.