A 5-digit combination lock can be opened only if a correct combination of digits is chosen. Find the probability of guessing the
1 answer:
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Answer:
Null hypothesis:
Alternative hypothesis:
Comparing the p value with the significance level assumed we see that
so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportions analyzed are significantly different at 5% of significance.
Step-by-step explanation:
Data given and notation
represent the number of people indicating that their financial security was more than fair in 2012
represent the number of people indicating that their financial security was more than fair in 2010
sample 1 selected
sample 2 selected
represent the proportion estimated of people indicating that their financial security was more than fair in 2012
represent the proportion estimated of people indicating that their financial security was more than fair in 2010
represent the pooled estimate of p
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
significance level given
Part a: Concepts and formulas to use
We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Hypothesis testing
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the statistic
Replacing in formula (1) the values obtained we got this:
Statistical decision
Since is a two sided test the p value would be:
Comparing the p value with the significance level assumed we see that
so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportions analyzed are significantly different at 5% of significance.