The price of an Ice cream cone is $3.25, but it cost $3.51 with tax. What is the sales tax rate?
2 answers:
Answer:
The correct answer is 8 %.
Step-by-step explanation:
We have a product that costs 3.25. Including the tax, the total amount of this product will be 3.51.
Now we must find out what was the percentage applied to the ice cream.
We do it as follows:
We know that the total tax was 0.26.
To find out the percentage we will use the formula
Where P represents the percentage we want to obtain, B is the value of the tax, and A is the value of the product without the tax.
We multiply that result by 100.
P =
In this way we can show that 8% is the percentage applied.
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Answer:
1. H0: P1 = P2
2. Ha: P1 ≠ P2
3. pooled proportion p = 0.542
4. P-value = 0.0171
5. The null hypothesis failed to be rejected.
At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .
6. The 99% confidence interval for the difference between proportions is (-0.012, 0.335).
Step-by-step explanation:
We should perform a hypothesis test on the difference of proportions.
As we want to test if there is significant difference, the hypothesis are:
Null hypothesis: there is no significant difference between the proportions (p1-p2 = 0).
Alternative hypothesis: there is significant difference between the proportions (p1-p2 ≠ 0).
The sample 1 (science), of size n1=135 has a proportion of p1=0.607.
The sample 2 (math), of size n2=92 has a proportion of p2=0.446.
The difference between proportions is (p1-p2)=0.162.
The pooled proportion, needed to calculate the standard error, is:
The estimated standard error of the difference between means is computed using the formula:
Then, we can calculate the z-statistic as:
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
As the P-value (0.0171) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .
We want to calculate the bounds of a 99% confidence interval of the difference between proportions.
For a 99% CI, the critical value for z is z=2.576.
The margin of error is:
Then, the lower and upper bounds of the confidence interval are:
The 99% confidence interval for the difference between proportions is (-0.012, 0.335).