A consumer advocate agency is concerned about reported failures of two brands of MP3 players, which we will label Brand A and Brand B. In a random sample of 197 Brand A players, 33 units failed within 1 year of purchase. Of the 290 Brand B players, 25 units were reported to have failed within the first year following purchase. The agency is interested in the difference between the population proportions, , for the two brands. Using the data from the two brands, what would be the standard error of the estimated difference, Dp = A – B, if it were believed that the two population proportions were, in fact, equal (i.e., )?

The standard error of the estimated difference is of 0.0313.

Step-by-step explanation:

To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Brand A:

33 out of 197, so:

Brand B:

25 out of 290, so:

What would be the standard error of the estimated difference?

The standard error of the estimated difference is of 0.0313.

Hana decided to pay down payment which is 15% of the total value of the car
DP = be the down payment amount
DP= 0.15 * $28,000
DP=$4200
The bank offers Hana a 48 months loan at 6.76%.
IA=Interest Amount
Solving for the monthly payment is shown below:
MP=Monthly Payment
MP= ((($28,000-$4200)*0.067 ) + ($28,000-$4200))/48 months
MP=(($23800*0.0676)+$23800) / 48 months
MP=$25408.88/48
MP=$529.352
Therefore, the monthly payment is $529.352.