Statistics - Hypothesis Testing, Percentile, Central Limit Theorem, Correlation Coefficient, Chi Square Test

STATISTICS
STUDENT ID:
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Question 1
The null hypothesis refers to the hypothesis that tends to support the non-existence of any
significance in the underlying observations. Hence, it tends to highlight that observations are
derived owing to chance and thereby do not signify any deviation from the hypothesised
population mean. This is indicated by H0 and assumed to be true in case of any hypothesis
testing unless proved false through existence of sufficient evidence based on the given
significance level.
Question 2
The alternative hypothesis tends to represent the hypothesis that the underlying deviation or
relationship is of significance. In research, usually the claim that is to be tested is usually
represented by the alternative hypothesis. If this is proved to be true, then it implies that the
observations are not by chance but infact tend to highlight a significant deviation from the
null hypothesis. Only when the null hypothesis is rejected can this be assumed to be true.
Question 3
Type 1 error refers to the rejection of a true null hypothesis. The probability of this error is
represented using the significance level or α. Also, lower the value of α, higher would be the
confidence level which is captured by 1 –α. Hence, if the probability of Type 1 error is lesser,
it would imply higher confidence with regards to the rejection of null hypothesis and
significance of observations.
Question 4
Type II error refers to the situation when a false null hypothesis is not rejected. The
probability of Type II error is indicated by 1 –β where β captures the test power. In order to
reduce Type II error, the sample size or n needs to be increased which would reduce the
standard error.
Question 5
a) The requisite screenshot for computation of 85 percentile is indicated below.

From the above output, 85 percentile lies at 170,728.63 miles.
b) The z score for the above mileage is computed below.
Z score = (170728.63-150000)/20000 = 1.0364
c) The relevant screenshot is shown below.

From the above, it is apparent that the requisite probability is 0.1524.
d) As per Central Limit Theorem, σxbar = σ/√n
Hence, sample standard deviation = 20000/√25 = 4000 miles
e) The requisite screenshot is shown below.