49. if a statistician specifies a 5% level of significance, then she will reject the null hypothesis only if her sample result differs from her hypothesized value by an amount that would occur by chance a) less than 5% of the time. b) more than 5% of the time. c) 95% of the time or more. d) 2.5% of the time or less.

The answer is a) less than 5% of the time

Step-by-step explanation:

By definition, the level of significance is the probability that one rejects a null hypothesis of a test when it is true. Denoted as alpha α, it shows how convincing the sample data is and concludes if it is statistically significant.

A level of significaance of 5% or 0.05, shows that you need more convincing power before determining whether you willreject the null hypothesis

By way of rule,

-If p-value ≤ level of significance α , then reject the null hypothesis.

-If p-value ≥ level of significance α , then do not reject the null hypothesis.

This implies that a statistician with a 5% level of significance will reject the null hypothesis if her hypothesized value falls below this mark.

c) 95% of the time or more.

Step-by-step explanation:

The level of significance in a statistical research is the probability of rejecting the null hypothesis when it is actually true. A possible example is a significance level of 0.02 which indicates a 2% risk of concluding that a difference exists when there is no actual difference. The lower the significance level, the stronger the evidence required before you can reject the null hypothesis. 5% significance level may imply 95% confidence interval which means the range of values that occurs 95% of the time.

Therefore, rejecting the null hypothesis at 5% significance level means that the alternative hypothesis differs from the null hypothesis by 95% or more of its possible values (95% of the time or more).

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