Question

**BASIC STATS FOR PSYCHOLOGY**

**Conceptual Questions**

a. When samples are taken at random and the sample sizes are reasonably large the sampling distribution of the mean will always be _____________.

b. All other things being equal, as the sample size ____________, the standard error of the mean will decrease.

c. To use the z test to compare means, one must know the population mean, the __________, and the_________.

Answer #1

a.The central limit theory states that when the sample sizes are reasonably large the sampling distribution of the mean follow a normal probabiity distribution and tend to cluster around the true population mean.

Answer. Normal.

b. The standard error of the mean which is also called the standard deviation of the mean becomes smaller when the sample size increases.

Answer. increases.

c. Z test is used for large sample to compare means. For one must know the the population mean, the size of the sample and the standard deviation.

Answer. size of the sample, standard deviation.

15. Random samples of size 81 are taken from an infinite
population whose mean and standard deviation are 200 and 18,
respectively. The distribution of the population is unknown. The
mean and the standard error of the mean are (assuming infinite
population)
a. 200 and 18
b. 81 and 18
c. 9 and 2
d. 200 and 2
16. A population has a mean of 300 and a standard deviation of
18. A sample of 144 observations will be taken....

consider the following results frmo two independent random
samples taken from two populations. assume that the variances are
NOT equal.
Population 1
population 2
sample size
50
50
sample mean
35
30
sample variance
784
100
a) what is the "degrees of freedom" for these data?
b) what is the 95% confidence interval difference of the
population means?

In order to compare
the means of two normal populations, independent random samples are
taken of sizes n1 = 400 and n2 = 400. The
results from the sample data yield:
Sample 1
Sample 2
sample mean = 5275
sample mean = 5240
s1 = 150
s2 = 200
To test the null
hypothesis H0: µ1 - µ2 = 0 versus
the alternative hypothesis Ha: µ1 -
µ2 > 0 at the 0.01 level of significance, the most
accurate statement...

(S 11.1) Random samples of sizes n1 = 405 and n2 = 311 were
taken from two independent populations. In the first sample, 120 of
the individuals met a certain criteria whereas in the second
sample, 131 of the individuals met the same criteria. Run a
2PropZtest to test whether the proportions are different, and
answer the following questions.
What is the value of p?, the pooled sample proportion?.
.3505586 Round your response to at least 3 decimal
places
Calculate...

Random samples of sizes n1 = 400 and n2 = 315 were taken from
two independent populations. In the first sample, 115 of the
individuals met a certain criteria whereas in the second sample,
123 of the individuals met the same criteria. Run a 2PropZtest to
test whether the proportions are different, and answer the
following questions. What is the value of p−, the pooled sample
proportion?Round your response to at least 3 decimal places. Number
Calculate the z test...

Consider the following results for independent random samples
taken from two populations.
Sample 1
Sample 2
n 1 = 20
n 2 = 40
x 1 = 22.1
x 2 = 20.9
s 1 = 2.4
s 2 = 4.7
What is the point estimate of the difference between the two
population means (to 1 decimal)?
What is the degrees of freedom for the t distribution
(round down your answer to nearest whole number)?
At 95% confidence, what is the...

Consider the following results for independent random samples
taken from two populations.
Sample 1
Sample 2
n 1 = 10
n 2 = 30
x 1 = 22.5
x 2 = 20.5
s 1 = 2.5
s 2 = 4.6
What is the point estimate of the difference between the two
population means (to 1 decimal)?
What is the degrees of freedom for the t distribution
(round down your answer to nearest whole number)?
At 95% confidence, what is the...

Consider the following results for independent random samples
taken from two populations.
Sample 1
Sample 2
n 1 = 10
n 2 = 30
x 1 = 22.5
x 2 = 20.5
s 1 = 2.5
s 2 = 4.6
What is the point estimate of the difference between the two
population means (to 1 decimal)?
What is the degrees of freedom for the t distribution
(round down your answer to nearest whole number)?
At 95% confidence, what is the...

1.14. A random sample of 22 shearing pins is taken in a study
of the Rockwell hardness of the pin head. Measurements on the
Rockwell hardness are made for each of the 22, yielding an average
value of 58.50 with a sample standard deviation of 15.5. Assuming
the measurements are normally distributed.
Construct a 95% two-sided confidence interval for the mean
Rockwell hardness. (2 Points)
If true standard deviation is equal to 12, how large a sample
size is necessary...

suppose a random sample of 25 is taken from a population that
follows a normal distribution with unknown mean and a known
variance of 144. Provide the null and alternative hypothesis
necessary to determine if there is evidence that the mean of the
population is greater than 100. Using the sample mean ybar as the
test statistic and a rejection region of the form {ybar>k} find
the value of k so that alpha=.15 Using the sample mean ybar as the...

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