Statistical Business Relevant

Since the mean and median are not equal, hence the given distribution is not normal and would have a definite skew. Infact a negative skew value suggests that the data is skewed towards the left side. The centre of the distribution would be at the mean value of 0.692.

The spread of the given data is very high as indicated from the high value of range and standard deviation. An appropriate parameter in this regard would be the coefficient of variation.

Coefficient of variation = Standard Deviation/Mean = 4.143/0.692 = 5.99

Clearly, this indicates that the spread of the distribution is very large.  However, this is on expected lines considering the nature of data which deals with stock markets returns over a long period.

2. The appropriate statistical test that should be used is the one sample t-test. The mean of the given salary is being compared to another fixed mean of $ 75,000.

H₀ : The average salary in Newscastle is equal to $ 75,000

H₁: The average salary in Newscastle is greater than $ 75,000

The relevant p value for single tail test is 0 and therefore is lower than the significance level of 5%. Hence, the null hypothesis should be rejected and alternate hypothesis should be accepted. Further, this conclusion can also be derived on the basis of the critical value test.

Type 1 error implies the situation when the true null hypothesis is rejected. In the given case, since the p value is zero, hence the possibility of conducting a type 1 error is also nill. Even at 0% significance level, the null hypothesis would be rejected without any second thoughts.

3. Incidence of assaults = 4109.114 + 99.248(Temperature in degree Celsius) + 6.704 (Number of police members)

Unemployment is not taken since it is not a significant variable.

The high F value of 178.82 with a corresponding value of p=0 clearly indicates that the model is significant. As a result, atleast one of the independent variable impacts the dependent variable and the coefficients of the independent variables cannot be assumed to be zero.

A R square value of 0.753 indicates that 75.3% of the change in the dependent variable (i.e. the incident of assault) can be explained on the changes in the independent variable.(i.e. number of police and temperature)

The hypotheses are as follows.

Null Hypothesis: H_o: The regression coefficient of temperature is zero.

Alternative Hypothesis: H₁: The regression coefficient of temperature is non-zero.

The test results are reflected by the t statistic and the consequent p value of 0.

Since, the p value is lower than significance level of 5%, hence the null hypothesis would be rejected and thus it indicates that that temperature is a significant variable. Hence, it may be concluded that the regression coefficient of temperature is non-zero and hence significant.

4. The relevant statistical test to test whether there is a difference in the satisfaction levels across location is ANOVA. Using the given data which captures the variation between groups, the given problem can be tested by framing appropriate hypothesis.

Null Hypothesis: The mean satisfaction level across all locations is the same

Alternative Hypothesis:  At least one location has a different mean satisfaction level than others.

Yes, the null hypothesis should be rejected since the obtained p value of 0.004 after the ANOVA test is lower than the significance level of 5%,

Hence, the rejection of null hypothesis implies that alternative hypothesis is true. Hence, the conclusion is that there is indeed difference in the mean satisfaction level across the given locations.

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