Question

Use a? t-test to test the claim about the population mean mu at the given level of significance alpha using the given sample statistics. Assume the population is normally distributed. ?Claim: muequals51 comma 700?; alphaequals0.01????Sample? statistics: x overbarequals51 comma 436?, sequals1800?, nequals20

Answer #1

Here we assume the population is normally distributed.

So we can use t test statistic formula for small n also

Formula of t test statistic is given by:

Where = sample mean = 51436

= population mean under null hypothesis = 51700

s = sample standard deviation = 1800

n = sample size = 20

Plug these values in the above formula, we get

Degrees of freedom = n - 1 = 20 - 1 = 20

p-value = "=TDIST(0.6559,19,2)" = 0.5197 (This is the p-value for two tail test

Decision rule:

1) If p-value < level of significance ( ) then we reject null hypothesis.

2) If p-value > level of significance ( ) then we fail toreject null hypothesis.

Here p - value = 0.5197 > 0.01 so we fail to reject the null hypothesis.

Conclusion : At 1% level of significance there is not sufficient evidence to reject the mean is 51700.

Use technology and a t-test to test the claim about the
population mean mu at the given level of significance alpha using
the given sample statistics. Assume the population is normally
distributed. Claim: mu greater than 74; alpha=0.01 Sample
statistics: x overbar=76.5, s=3.4, n=26

Use a t-test to test the claim about the population mean μ at
the given level of significance α using the given sample
statistics. Assume the population is normally distributed.
Claim: μ=51,300; α=0.10 Sample statistics:
x overbar =52,024
s=2,100
n=19

Test the claim about the population mean mu at the level of
significance alpha. Assume the population is normally
distributed.
Claim: u > 25; alpha = 0.05; sigma=1.2
Sample statistics: x overbar=25.3, n=50

Test the claim about the population mean, mu , at the given
level of significance using the given sample statistics. Claim: mu
equals30; alpha equals0.07; sigma equals3.28. Sample statistics:
x overbar equals28.3, equals 67

Test the claim about the population mean ? at the given level of
significance using the given sample statistics. Assume the
population is normally distributed. Be sure to identify the null
and alternative hypotheses. Claim: u=200, alpha= 0.05 Sample
Statistics: x overbar= 210, s=30, n=16

Use technology and a t-test to test the claim about the
population mean muμ at the given level of significance
alphaα using the given sample statistics. Assume the population
is normally distributed.
Claim: muμgreater than>7474 ; alphaα=0.010
Sample statistics:
x bar=74.374.3 , s=2.92.9 , n=26
What is the p-value of the test statistic?

Use a t-test to test the claim about the population mean μ at
the given level of significance α using the given sample
statistics. Assume the population is normally distributed.
Claim: μ ≠ 24; α=0.10 Sample statistics: x overbar =
21.4, s = 4.2 , n equals = 11
What are the null and alternative hypotheses? Choose the
correct answer below.
A.H0: μ≠24
Ha: μ=24
B.H0: μ≤24
Ha: μ>24
C.H0: μ=24
Ha: μ≠24
D.H0: μ≥24
Ha: μ than<24...

test the claim about the population mean u at the level of
significance a. assume the population is normally distributed claim
u=1660 a=0.01 o=82 sample statistics x=1630 n=35

In exercise #36 ,test the claim about the population
mean μ at the level of significance a.
Assume the population is normally distributed. If convenient, use
technology.
Exercise #36
Claim: μ < 850; a =
0.025. sample statistics: x = 875, s = 25, n = 14

Test the claim about the population mean,
muμ,
at the given level of significance using the given sample
statistics.
Claim:
muμequals=5050;
alphaαequals=0.090.09.
Sample statistics:
x overbarxequals=48.848.8,
sequals=3.793.79,
nequals=79

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