Use the graph of the polynomial function to find the factored form of the
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The price of the sweater was reduced by 40%
Step-by-step explanation:
Step 1; Cost before reduction was $20. The cost after reduction was 12$. Cost reduced= cost before reduction - cost after reduction
Cost reduced= $20 - $12 = $8
Step 2; We must find how much of the cost was reduced from the initial cost i.e. how much $8 is to $20. To do this we must convert it into a percentage. We divide the $8 with the $20 to get a value. This value must be multiplied with a 100 to be converted into a percentage.
Cost by which sweater was reduced= * 100 = 0.4 * 100 = 40
So the price of the sweater was reduced from $20 to $8 which equates to a reduction in 40%.
Answer:
1) A. H0: p = 0.30
HA: p not equal to 0.30
2) A. The Independence Assumption is met.
C. The Randomization Condition is met.
D. The Success/Failure Condition is met.
3) Test statistic z = 2.089
P-value = 0.0367
4) C. Reject H0. There is sufficient evidence to suggest that the percentage of bills paid by medical insurance has changed.
Step-by-step explanation:
1) This is a hypothesis test for a proportion.
The claim is that there is a significant change in the percent of bills being paid by medical insurance.
As we are looking for evidence of a difference, no matter if it is higher or lower than the null hypothesis proportion, the alternative hypothesis is defined by a unequal sign.
Then, the null and alternative hypothesis are:
2) Cheking the conditions:
The independence assumption and the randomization condition are met as the bills were selected randomly from the population.
The 10% condition can not be checked, as we do not know the size of the population.
The success/failure condition is met as the products np and n(1-p) are bigger than 10 (the number of successes and failures are both bigger than 10).
3) The significance level is assumed to be 0.05.
The sample has a size n=9260.
The sample proportion is p=0.31.
The standard error of the proportion is:
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:
As the P-value (0.0184) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that there is a significant change in the percent of bills being paid by medical insurance.