Question

1) Determine whether the following hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither.

Claim about IQ scores of statistics instructors: μ > 100.

Sample data: n = 15, x ¯= 118, s = 11.

The sample data appear to come from a normally distributed population with unknown μand σ.

a) student T-distribution

b) Normal distribution

c) Neither

2)

Determine whether the following hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither.

Claim about daily rainfall amounts in Boston: μ < 0.20 i n c h e s

Sample data: n = 19, x ¯= 0.10in, s = 0.26 in.

The sample data appear to come from a population with a distribution that is very far from normal, and σis unknown.

a) Student T-distribution

b) Normal distribution

c) Neither

3)

Determine whether the following hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither.

Claim about daily rainfall amounts in Boston: μ < 0.20 i n c h e s

Sample data: n = 52, x ¯= 0.10in, s = 0.26 in.

The sample data appear to come from a population with a distribution that is normal, and σis known.

a) Student T- distribution

b) Normal distribution

c) neither

4.)

The U.S. Mint has a specification that pennies have a mean weight of 2.5 g. A sample of 37 pennies has a mean weight of 2.49910 g and a standard deviation of 0.01648 g. Use a 0.05 significance level to test the claim that this sample is from a population with a mean weight equal to 2.5 g. Do the pennies appear to conform to the specifications of the U.S. Mint?

Which of the following are the correct hypotheses?

a) H 0 μ = 2.5 H 1 μ ≠ 2.5

b) H 0 μ = 2.5 H 1 μ > 2.5

c) H 0 μ = 2.5 H 1 μ < 2.5

Answer #1

Determine whether the hypothesis test involves a sampling
distribution of means that is a normal distribution, Student t
distribution, or neither. Claim: ? = 119. Sample data: ? = 15, ?̅ =
103, ? = 15.2. The sample data, for this simple random sample,
appear to come from a normally distributed population with unknown
? and ?.

Determine whether the hypothesis test involves using a
normal distribution, Student t distribution, or
neither.
Claim: μ = 981. Sample data: n = 15, = 972, s =
26.
The sample data appear to come from a normally distributed
population with unknown σ.
Select one:
Neither normal nor t-distribution
Student's t-distribution
Normal distribution

Claim u = 977. Sample data: n = 25 and xbar = 984, s =
25. The sample data appear to come from a normally distributed
population with o = 28. Does the hypothesis test involve sampling
distribution of means that is normal, student t or neither?

Determine which distribution should be used in a
hypothesis test with the following information, or if it is not
appropriate to conduct a hypothesis test.
(a) The claim is μ
≤ 86. The sample data is: n = 29, ¯x
= 85.2, and s = 8. The population standard deviation is
unknown, and the population is not even approximately normally
distributed.
Normal (z) distribution (or
Z-Test on the calculator)
Student t distribution (or
T-Test on the calculator)
A...

Can a normal approximation be used for a sampling distribution
of sample means from a population with μ=53 μ=53 and σ=9 σ=9 , when
n=64 n=64 ?

Decide whether the normal sampling distribution can be used. If
it can be used, test the claim about the population proportion p
at the given level of significance
alphaα
using the given sample statistics.Claim:
pnot equals≠0.24;
alphaαequals=0.10;
Sample statistics:
ModifyingAbove p with caretpequals=0.21,
nequals=200
Can the normal sampling distribution be used?
state the null and alternative hypothesis.
determine the critical value.
find the z-test statistic.
what is the result of the test?
Reject
Upper H 0H0.
The data provide sufficient...

For the following information, determine whether a normal
sampling distribution can be used, where p is the population
proportion,α is the level of significance, ModifyingAbove p with
caretp is the sample proportion, and n is the sample size. If it
can be used, test the claim. Claim:
p>0.29
α=0.08
Sample statistics:
ModifyingAbove p with caretpequals=0.36
n=375

Decide whether the normal sampling distribution can be used. If
it can be used, test the claim about the difference between two
population proportions p 1 and p 2 at the given level of
significance alpha using the given sample statistics. Assume the
sample statistics are from independent random samples. Claim: p
1equalsp 2, alphaequals0.01 Sample statistics: x 1equals27, n
1equals129 and x 2equals32, n 2equals206 Can a normal sampling
distribution be used?

Question 2: Which of the following statements about the
sampling distribution of means is not true?
A. A sample distribution's mean will always equal the parent
population distribution's mean
B. The sampling distribution of means approximates the normal
curve.
C. The mean of a sampling distribution of means is equal to the
population mean.
D. The standard deviation of a sampling distribution of means is
smaller than the standard deviation of the population.

For the following information, determine whether a normal
sampling distribution can be used, where p is the population
proportion,
alphaα
is the level of significance,
ModifyingAbove p with caretp
is the sample proportion, and n is the sample size. If it can
be used, test the claim.Claim:
pgreater than or equals≥0.47
alphaαequals=0.06
Sample statistics:
ModifyingAbove p with caretpequals=0.40,
nequals=180

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