Question

1. In R, inverse probability distribution functions start with q
(no reason why really; it’s just a convention). To calculate the
critical value for a two-tailed *t-test* with *n*
*− k* = 100 and *α* = 0.05, use the inverse
*t* distribution command. For the inverse t function, type
qt(1-0.05/2, 100). To find the one-tailed critical value for a
*t* distribution for *α* = 0.01 and 100 degrees of
freedom, type qt(1-0.01, 100).

2. To find the critical value from a normal distribution for a given a, use the inverse normal function in R. For a two-sided test, type qnorm(1-a/2). For a one-sided test, type display qnorm(1-a).

**3.**The *p-value* reported in summary(lm(Y
∼ X1)) is a two-sided *p-value*. To generate the *p*
values from the *t* statistic only, use 2*(1-pt(abs(TSTAT),
DF)), where TSTAT is the observed value of the *t* statistic
and DF is the degrees of freedom. For example, for a two-sided
*p-value* for a *t* statistic of 4.23 based on 1,908
degrees of freedom, type 2*(1-pt(abs(4.23), 1908)).

Answer #1

1.
lm(EARNINGS~S+EXP) (in R),
the underlying assumption was that EARNINGS is a normally
distributed random variable with an expected value given by a
constant, but unknown value (represented by the Greek letter "mu")
that we are trying to estimate.
True or False?
2.
In our typical simulation program, when we save some number like
1,000 or 10,000 replications for some statistic like a t-ratio or
an F-statistic, the purpose of a summary command such as
mean(abs(ts) > qt(.975,df) ) or...

Determine if the statements below are true or false:
The chi-square distribution, just like the normal distribution,
has two parameters, mean and standard deviation.
The chi-square distribution is always right skewed, regardless
of the value of the degrees of freedom parameter.
The chi-square statistic is always positive.
As the degrees of freedom increases, the shape of the chi-square
distribution becomes more skewed.
"If you found χ2 = 10 with df = 5, you would fail to reject the
Null hypothesis...

(a) Suppose n = 6 and the sample correlation
coefficient is r = 0.894. Is r significant at the
1% level of significance (based on a two-tailed test)? (Round your
answers to three decimal places.)
t
=
critical t
=
Conclusion:
Yes, the correlation coefficient ρ is significantly
different from 0 at the 0.01 level of significance.
No, the correlation coefficient ρ is not significantly
different from 0 at the 0.01 level of
significance.
(b) Suppose n = 10 and...

Short Answer Questions: (Try to answer these 8 questions
without using software or tables.)
In the standard normal and t distributions, the 95% confidence
multiplier is equal to the ___________ 1-sided critical value.
In the standard normal and t distributions, the 1-sided 5%
critical value is equal to the ___________% confidence
multiplier.
In the standard normal and t distributions, which is larger,
the 1-sided 5% critical value or the 1-sided 1% critical value?
Answer: ____________
In the standard normal and...

(1) Consider a Chi-square distribution with degrees of freedom,
df =7 I What is the mean?; II. the standard deviation, for this
distribution?
(2) Consider a Chi-square distribution for a categorical
variable with 4 levels. I. What is the degrees of freedom for this
distribution? II. The chi-square test statistic was calculated to
be 8.012. What is the p-value for this distribution?

Suppose you conduct a hypothesis test for the following
hypotheses from a sample of n = 25 observations, and you calculate
a test statistic of t = 1.75. (2 points each)
H0: m = 0
Ha: m > 0
What are the degrees of freedom for this statistic?
What are the two critical values t* from the t-Distribution
Critical Values table that bracket this test statistic? What are
the one-sided p-values for these two entries?
Is the value t =...

you are calculating a confidence interval for the population
mean. Find the critical value t* from the t-Distribution Critical
Values table for each of the following situations
A 95% confidence interval based on n = 12 observations.
A 99% confidence interval from a sample of two observations.
A 90% confidence interval from a sample of size 1001.
2. Suppose you conduct a hypothesis test for the following
hypotheses from a sample of n = 25 observations, and you calculate
a...

Question 1
The main reason a research uses a t-test instead of a z-test is
when little is known about population (mean and standard
deviation).
1) True
2) False
Question 2
Values in the t‐table are not actually listed by sample
size but by degrees of freedom (df).
1) True
2) False
Question 3
A 90 percent confidence level is equivalent to an alpha level of
0.10
1) True
2) False
Question 4
A professor wants to know if her...

13. A 0.01 significance level is used for a hypothesis test of
the claim that when parents use a particular method of
genderselection, the proportion of baby girls is greater than 0.5.
Assume that sample data consists of 55 girls in 100 births, so the
sample statistic of 11/20 results in a z score that is 1 standard
deviation above 0. Complete parts (a) through (h) below
A. Identify the null hypothesis and the alternative hypothesis.
Choose the correct answer...

1. You have a two-tailed test. The t critical value is 2.36 and
the test statistic is 3.11. Assume the null hypothesis is true. The
result is (a) Type I error (b) Type II error (c) Correct
decision
2. You have a right-tailed test. The t critical value is 1.74
and the test statistic is 1.46. Assume the null hypothesis is true.
The result is (a)Type I error (b) Type II error (c) Correct
decision
3. You have a right-tailed...

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