Dr. Montgomery recently graduated from medical school and his wife bought him an engraved stethoscope. The stethoscope cost $160
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Answer:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is significantly higher than 0.5.
Step-by-step explanation:
Data given and notation
n=502 represent the random sample taken
X=331 represent the adults that said they would not be bothered if the NAtional security agency
estimated proportion of people who would not be bothered if the NAtional security agency
is the value that we want to test
represent the significance level
Confidence=99% or 0.99
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is higher than the majority of 0.5:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is significantly higher than 0.5.
The amount that is the closest to the account balance at the end of 4 years is given by: Option B: $5,860. 53 (approx)
<h3>How to calculate compound interest's amount?</h3>If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
The final amount becomes:
For the considered case, we're given that:
- Initial amount Laura deposited = $5,500 = P
- Type of interest: Compound interest
- Unit of time: Annually
- Rate of interest = 1.6% annually = R
- Total unit of time for which amount is to be calculated: 4 years = T
The final amount at the end of 4 years in the considered account of Laura is evaluated as:
Thus, he amount that is the closest to the account balance at the end of 4 years is given by: Option B: $5,860. 53 (approx)
Learn more about compound interest here: