Understanding Null Hypothesis, Alternative Hypothesis, Type I and Type II Errors in Statistics

Question 1
(1) Null hypothesis in statistics represents the hypothesis that supports the claim related
to the non-existence of any significance regarding any observation or claim. It
constitutes the observations that have derived by chance and thus, there is no
significance deviation as compared with the hypothesized mean (population mean).
Null hypothesis is represented through symbol (H0). Null hypothesis assumed to be
true only unless the hypothesis test conducted and sufficient statistical evidence
present at a specified significance level to reject it.
(2) Alternative hypothesis in statistics refers to the hypothesis that supports the claim of
some observation or significant relationship between the variables. The research
claims are generally represented in alternative hypothesis only. When the hypothesis
test result provides sufficient evidence to accept the alternative hypothesis then it
would be said that the observation is not by chance. Alternative hypothesis
represented through symbol (Ha or H1) and would be true only when the null
hypothesis rejected.
(3) Type I errors implies the rejection of true null hypothesis. The probability of type I
error indicated by significance level represented as alpha. When the value of alpha is
lowest then the corresponding confidence level would be higher. The confidence level
would be found through (1- alpha). When the type I error (alpha) is significantly
lower than there would be higher confidence to reject the null hypothesis.
(4) Type II errors implies the scenario when of false null hypothesis would not be
rejected. The probability of type II error indicated by1- beta where the beta is the test
power. The type II error can be minimized by increasing the sample size because the
standard error would be reduced by increasing the sample size.
Standard error ∝= 1
√n
Question 5
Mean truck weights = 20,000 lbs
Standard deviation = 2000 lbs
Distribution approximates a bell curve which implies that the truck weight distribution
follows normal distribution.
(a) The maximum mileage of a car which is 80th percentile is computed through z table
calculation and is shown below.
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(b) The z score for this mileage
z−score= x−μ
σ
z score=21682.913−20000
2000 =0.841
(c) Probability that a randomly selected truck’s weight would fall between 21000 and 22000
miles
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There is 0.1499 probability that a randomly selected truck’s weight would fall between 21000
and 22000 miles.
(d) Number of trucks = 16
Standard deviation of sample ¿ σ
√ n =2000
√16 =500 miles
(e) Probability that a randomly selected truck’s weight would fall between 21000 and 22000
miles from a group of 16 trucks
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There is 0.0227 probability that a randomly selected truck’s weight would fall between 21000
and 22000 miles from a group of 16 trucks.
Question 6
a) Null hypothesis H0: μ = 10
b) Alternative hypothesis Ha: μ>10
c) Based on the sign of the alternative hypothesis, it can be said that the hypothesis test is a
right tailed hypothesis test.
d) Mean of sample (using Excel) x bar = 10.30
e) Standard deviation of sample (using Excel) s = 2.85
f) Sample size = 20
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