Question

For each of the following statements, identify whether the statement is true or false, and explain why. Please limit each response to no more than 3 sentences.

i) A p-value is the probability that the null hypothesis is false. ii) A chi-square test statistic can never be negative.

iii) If we reject the null hypothesis that a population proportion is equal to a specific value, then that specific value will not be contained in the associated confidence interval.

iv) If we reject the null hypothesis that the population mean is less than or equal to 1 at the 1% level of significance, then the lower bound of the associated 99% confidence interval will be greater than 1.

v) In simple linear regression, the fitted slope will always have the same sign (i.e. positive or negative) as the sample correlation.

Answer #1

i)false( it is probability of getting as or more exrteme test statisitc if null is true)

ii) true ( since chi square distribution start with 0 values , therefore it can not be negative)

iii) true (since confidence interval and hypothesis test gives the same result, therefore rejecting the null also means that confidence interval will not contain the given value)

iv) true (since confidence interval and hypothesis test gives the same result)

v) true (since both slope and corerlation coeffiicient sign represent the direction of linear trend)

For each of the following statements, identify whether the
statement is true or false, and explain why. Please limit each
response to no more than 2 sentences.
f) A weighted mean is preferred over an unweighted mean (i.e. a
regular sample mean) when each observation has its own unique
weight.
g) A z-score is a percentile.
h) Assuming the population is normally distributed, the standard
deviation of the sampling distribution of the sample mean will
always be less than or...

Identify each of the following statements as either true of
false.
a) FalseTrueClick for
List If the null hypothesis is false, then
large differences between the observed and expected values may
exist.
b) FalseTrueClick for
List In a one-way table, each observed value
can fall into only one of the given classifications.
c) FalseTrueClick for
List To determine the expected frequency for
each cell, we multiply the total number of observations by the
probability of an observation being in that particular cell.
d) ...

Suppose that a researcher, using data on class size (CS) and
average test scores from 50 third-grade classes, estimates the OLS
regression ModifyingAbove TestScore with caret equals 672.315 +
left parenthesis negative 5.1765 right parenthesistimesCS, Upper R
squared = 0.09, SER = 9.1 (24.675) (2.0806) Construct a 95%
confidence interval for beta 1, the regression slope coefficient.
The 95% confidence interval for beta 1, the regression slope
coefficient, is ( nothing, nothing). (Round your responses to
two decimal places.) The...

1a. Suppose the value a is inside the 90% confidence interval
for a coefficient in an estimated regression. Suppose one were to
test the hypothesis that the coefficient is equal to a against the
two sided alternative that it is not equal to a. Which of the
following is a correct statement?
I would not reject the null at the 10% significance level
I would reject the null hypothesis at the 5% level of
significance
I would reject the null...

Determine whether the BEST, most common
interpretation of the given statement is:
TRUE - Select 1
FALSE - Select 2
Question 1 options:
1
Type II error is the probability of failing to reject H0 when it
is false.
2
In hypothesis testing, the ALTERNATIVE hypothesis states how the
parameter of interest differs from the null hypothesis value.
3
The p-value is determined by the ALTERNATIVE hypothesis.
4
The p-value is the probability the null hypothesis is true....

An estimated regression coefficient is equal to 0.5. What is the
confidence level associated with the one sided interval(0.5,∞)?
a. 50%
b. 95%
c. 100%
d. 90%
Suppose a hypothesized slope value is not contained in the 95%
confidence interval. If one were test the hypothesis at the 10%
level which of the following statements are correct?
a. I would reject the null hypothesis
b. I would not reject the null hypothesis
c. I need more information
Suppose the value...

True/False, if false briefly explain.
1. The margin of error for a confidence interval used for an
opinion poll does not take into account the fact that people who
did not answer the poll questions may have had different responses
from those who did answer the questions.
2. If the p-value for a significance test is 0.35, we can
conclude that the null hypothesis has a 35% chance of being
true.
3. A student project used a confidence interval to...

Indicate whether the following statement is true or false.
If we do not reject the null hypothesis, it is possible we have
made both type I and type II errors.
In an upper tail hypothesis test for the mean, the critical
value is 2.575 and the test statistic is 2.5. In this case, the
null hypothesis should not be rejected.
The calculated p-value should be divided by 2 to make the
decision for a two tail test.
The sampling error...

True or False: For all hypothesis tests, a small p-value means
we will reject the null.
True or False: If you are testing the means of two groups, then
you would use ANOVA.
True or False: A two-sample confidence interval must capture
zero to show the groups are different.
True or False: The test statistic for ANOVA is the
f-statistic.
True or False: For Chi-Square tests, if the observed counts and
expected counts are extremely different, then we would have...

Please answer true / false / uncertain to the statement and
EXPLAIN THE ANSWER.
Assume a regression coefficient has a p-value of 0.02. Then, at
95% confidence we reject the hypothesis that the true parameter is
zero. However, at 99% confidence we accept the same hypothesis.

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