Q1.
Sample size: 1000; sample proportion: 56%; confidence level: 95%. The construction of a confidence interval proportion procedure is based on the assumption that both np 10 and n (1- p ) a confidence interval for a population proportion is constructed by taking the point estimate ( p ˆ p^ ) plus and minus the margin of error. The margin of error is computed by multiplying a z multiplier by the standard error, SE ( p ˆ) SE (p^) . The multiplier associated with 95% confidence interval is 1.96. Therefore, confidence interval proportion of p is 0.56±1.96 ( ) = ±3.08
Q2.
The z* = 1.65.
Margin of error = (z*)(s) / sqrt n
2 days = (1.65)(14 days) / sqrt n, now solve for n ...
n = 133.4, always round up.
ANSWER is 134 outside salespeople should be sampled
Q3.
There are seven steps in statistical hypothesis testing as listed below:
Step 1: state the Null Hypothesis.
The null hypothesis is the opposite of the “guess” made by the research.
Step 2: state the Alternative Hypothesis.
The Alternative Hypothesis is stated merely because the Null Hypothesis might be rejected for many possibilities for instance, if a null hypothesis says that every mean differs from every other mean.
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Step 3: set α
Step 4: Collect Data
Data should be collected in remembrance of the significance of identifying whether the collected data is obtained through an observational or an experimental design.
Step 5: calculate a test statistic
F statistic is used for categorical treatment level means.
Step 6: construct acceptance or rejection regions
A threshold value of F is obtained from statistical tables and is known as F critical or Fα, which is the minimum value for the test statistic.
Step 7: based on steps 5 and 6, draw a conclusion about H 0
If the F calculated from the data is larger than the Fα, then you are in the Rejection region and you can reject the Null Hypothesis with (1-α) level of confidence.
Q4
State the null hypothesis and the alternate hypothesis.
Ho: u = >= 3
Ha: u < 3 (claim)
b) This is a left test
c)State the decision rule.
invT(0.05,49) = -1.6766
Reject Ho if the test statistic is less than -1.6766
d)Compute the value of the test static.
t(2.75) = (2.75-3)/[1/sqrt(50)] = -0.035
e)What is your decision regarding Ho?
Fail to reject Ho. The test results do not support the claim
that u < 1
f)What is the p-value? Interpret it.
P(t < -1.6766 when df = 49) = tcdf(-100,-0.035) = 0.0486
g)Since the p-value is less than 5%, reject Ho.
Q5
The test is right tailed test
H0: μ = 50 H1: μ ≠ 50
Standard deviation=6
.05 significance level
(.05,49)=-8.333
Since the value is more than 100%, decide Ho.
Q6
H0: μ ≤ 10 H1: μ > 10
This is a left tailed test
Standard deviation = 3
.01 significance level]
(.01,9)=-3.3333
Since the value is less than 50%, reject Ho.
Q7
H0: μ ≥ 20 HA: μ < 20
This is a two tailed test
Significance level =.05
(.05,19)=-12.5. decided.
Q8
It is reasonable to conclude that mean rate of return is more than 4.5%, using the .05 significance level, since the outcome is slightly above the 4.5%.
