MONICA PAID SALES TAX OF 1.50 WHEN SHE BOUGHT A NEW BIKE HELMET . IF THE SALES TAX RATE WAS 5% HOW MUCH DID THE STORE CHARGE FOR
1 answer:
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We will use the followin property of logarithms:
So, we have
If you multiply both sides by 4, you get
Answer:
Null hypothesis:
Alternative hypothesis:
Comparing the p value with the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant difference between the two proportions.
Step-by-step explanation:
1) Data given and notation
represent the number college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)
represent the number college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)
sample 1
sample 2
represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)
represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
significance level given
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if is there is a difference in the two proportions, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
3) Calculate the statistic
Replacing in formula (1) the values obtained we got this:
4) Statistical decision
Since is a two sided test the p value would be:
Comparing the p value with the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant difference between the two proportions.