8.1 hw

To get a​ two-sided p-value equal to​ 1, the​ t-statistic must be ___. The only way the​ t-statistic will be 0 is if the numerator is _____.

0, 0

A​ p-value is a probability. It is not possible to get a probability greater than

1

A medical study was investigating whether getting a flu shot actually reduced the risk of developing the flu. A hypothesis test is to be performed. Which of the following statements is​ correct?

A​ one-tailed test will be performed since the alternative hypothesis states that the parameter is less than the hypothesized value.

__________ are developed from a question of​ interest, which should be determined prior to collecting data.

Hypotheses

A student wondered if more than​ 10% of students enrolled in an introductory Chemistry class dropped before the midterm. He noticed that 2 out of 15 of his friends in the class dropped before the midterm. Based on his​ sample, he performed a hypothesis test. Is the hypothesis test a​ one-tailed or​ two-tailed test?

It is a​ one-tailed test since the alternative hypothesis states that the parameter is greater than the hypothesized value.

Typically, the idea of the​ _______ hypothesis is that of​ "no effect,"​ "no difference," or​ "no change."

Null =

When no significance level is given and the _______hypothesis is​ rejected, the probability of making a Type _________error is the​ p-value.

Null I

A medical study was investigating if getting a flu shot actually reduced the risk of developing the flu. A hypothesis test is performed. Which of the following will result in a Type I​ error?

Researchers said the flu shot reduced the risk of developing the flu when it actually​ didn't.

Jan performed a study and obtained a​ p-value of 1.24. What conclusion should Jan​ make?

She made an error since it is not possible to get a​ p-value of 1.24.

A high​ p-value indicates not enough evidence to reject the null hypothesis.

True

A​ p-value is the probability of observing a value of a statistic or a value that is more unusual just by chance only if the null hypothesis is ______

true

is the number of standard deviations an observation is from the mean.

z-score

A medical study was investigating if getting a flu shot actually reduced the risk of developing the flu. A hypothesis test is performed. Suppose the null hypothesis was rejected with a​ p-value of 0.0002. The power of the test was 0.90. What type of error could be made and what is the probability of making that​ error?

A Type I error could be made with a probability of 0.0002.

Ted wanted to determine if one brand of paper towels​ (Brand A) was stronger than another brand​ (Brand B). He performed a study where he randomly selected 25 sheets from each of the two​ brands, placed each sheet in an embroidery hoop​ (and tightened the​ hoop), placed 30 drops of water on each paper​ towel, and placed weights on each sheet until the sheet broke. He recorded the maximum weight on the paper towel before it broke. Suppose the null hypothesis was rejected at a significance level of 0.05. The power of the test was 0.80. What type of error could be made and what is the probability of making that​ error?

A Type I error could be made with a probability of 0.05.

A medical study was investigating if getting a flu shot actually reduced the risk of developing the flu. A hypothesis test is performed. Suppose the null hypothesis was not rejected at a significance level of 0.05. The power of the test was 0.85. What type of error could be made and what is the probability of making that​ error?

A Type II Error could be made with a probability of 0.15.

Suppose increasing the sample size will not change the sample mean or the standard deviation. What will happen to the​ p-value by increasing the sample​ size?

A. The​ p-value will decrease.

Typically, the direction ​(greater than>​, less than<​,or not equals≠​) used in the​ _______ hypothesis is determined from the question of interest.

Alternative

Ted wanted to determine if one brand of paper towels​ (Brand A) was stronger than another brand​ (Brand B). He performed a study where he randomly selected 25 sheets from each of the two​ brands, placed each sheet in an embroidery hoop​ (and tightened the​ hoop), placed 30 drops of water on each paper​ towel, and placed weights on each sheet until the sheet broke. He recorded the maximum weight on the paper towel before it broke. Which of the following statements is​ correct?

A​ two-tail test will be performed since the alternative hypothesis contains a​ "not equal​ to". Ted is not hypothesizing which brand is​ stronger, just that there is a difference in strength between the two brands.

Determine whether the following statement is true or false. It is good science to collect data before determining the null and alternative hypotheses.

FALSE

Researchers conducted a study and obtained a​ p-value of 0.75. Based on this​ p-value, what conclusion should the researchers​ draw?

Fail to reject the null hypothesis but do not accept the null hypothesis as true either.

Determine if the following statement is true or false. Researchers conducted a study and obtained a​ p-value of 0.30. Because the​ p-value is quite​ high, there is evidence to accept the null hypothesis.

False

Alex hypothesized​ that, on​ average, students study less than the recommended two hours per credit hour each week outside of class. Which of the following is​ Alex's alternative​ hypothesis?

H1: ü<2 hours per week per credit

A ________ p-value indicates that there is not enough evidence to reject the null hypothesis.​ But, it​ doesn't mean the ________ hypothesis should be accepted as true.

High Null

Benjamin performed a​ two-tailed one-sample​ t-test and obtained a p-value=1. What conclusion should he​ make?

His sample mean must have been exactly equal to his hypothesized value for the population mean.

A Type Error can only be made when there is not evidence to reject the null hypothesis.

II

Ted wanted to determine if one brand of paper towels​ (Brand A) was stronger than another brand​ (Brand B). He performed a study where he randomly selected 25 sheets from each of the two​ brands, placed each sheet in an embroidery hoop​ (and tightened the​ hoop), placed 30 drops of water on each paper​ towel, and placed weights on each sheet until the sheet broke. He recorded the maximum weight on the paper towel before it broke. Which of the following would result in a Type II​ error?

Ted found that neither brand of paper towels was stronger than the other when in fact one was stronger.

Nurses wondered if birth weights of babies are going up. They knew that the average birth weight of a baby last year was 7.6 pounds. A random sample of 65 weights of babies at the hospital where the nurses work gave an average birth weight of 7.9 pounds. Which of the following statements is​ true?

The nurses can use the sample data to make an inference about birth weights at this​ hospital, but should be cautious about making inferences about birth weights beyond this hospital.

Suppose x =​60, H0​: μx=​50, HA​: μx>​50, and the​ p-value from a​ one-sample test is 0.04. What does this​ p-value mean?

The probability of getting a sample mean of 60 or more if the true population mean is 50 is 0.04.

When are conclusions said to be​ "statistically significant"?

When the​ p-value is less than a given significance level This is the correct answer.

Determine if the following statement is true or false. If it is​ false, explain why. A​ p-value is the number of standard deviations an observation is from the mean.

This statement is false. The definition given is for the​ z-statistic. A​ p-value is the probability of observing a value of a statistic or a value that is more unusual just by chance if the null hypothesis is true.

Determine if the following statement is true or false. If it is​ false, explain why. A​ p-value is the probability that the null hypothesis is true.

This statement is false. The null hypothesis will either be true or it​ won't be true​ - there is no probability associated with this fact. A​ p-value is the probability of observing a sample mean​ (for example) that we did or something more unusual just by chance if the null hypothesis is true.

Determine if the following statement is true or false. If it is​ false, explain why. A​ p-value is the probability of accepting the null hypothesis.

This statement is false. We never accept the null hypothesis no matter what the​ p-value is. A​ p-value is the probability of observing a sample mean​ (for example) that we did or something more unusual just by chance if the null hypothesis is true.

The ___________ hypothesis typically goes with the claim being made or question asked.

alternative

The null and alternative hypotheses are determined __________ after before data are collected.

before

What is the difference between the null hypothesis value and the true value of a parameter​ called?

the effect size

Determine whether the statement is true or false. Researchers can make the results statistically significant by increasing the sample size even if the difference between the sample mean and hypothesized value of the population mean is very small.

true