A bank randomly selected 250 checking account customers and found that 110 of them also had savi

A bank randomly selected 250 checking account customers and...

Key Concepts

Standard Error

The standard error measures the variability of the sample proportion from the true population proportion. It is computed as the square root of the product of the sample proportion and its complement divided by the sample size, reflecting how stable the estimate is across different samples.

Margin of Error

The margin of error is the product of the critical value and the standard error. It quantifies the maximum expected difference between the sample estimate and the true population proportion at the given confidence level, thus setting the bounds of the confidence interval.

Critical Value

The critical value is a point on the probability distribution that corresponds to the desired confidence level. For a 95% confidence interval and assuming a normal distribution, the critical value is approximately 1.96, which determines the width of the interval when multiplied by the standard error.

Confidence Interval

A confidence interval provides a range of values that is likely to contain the true population parameter with a specified level of confidence, such as 95%. It is constructed by taking the point estimate and adding and subtracting the margin of error.

Sample Proportion

The sample proportion is an estimate of the true population proportion, calculated by dividing the number of successes (in this case, customers having both checking and savings accounts) by the total sample size. It serves as the point estimate around which the confidence interval is built.

Transcript

00:01 250 customers that have a checking account at a bank were surveyed and we found that 110 of those that had a checking account also had a savings account.

00:12 So let's calculate the 95 % confidence interval.

00:16 The first step in calculating a 95 % confidence interval is to describe the population parameter of interest.

00:24 So for this, we use p for abbreviation and we are looking that p can be described as the proportion of customers who also have a savings account.

00:42 So p is a proportion of customers who also have a savings account.

00:47 Step two is to check the assumptions.

00:52 So the sample was random.

00:55 They surveyed random customers at the bank.

01:00 Each response was independent because if the first person they surveyed had a savings account, that didn't affect whether the second person had a savings account.

01:09 And the two other conditions that we want to test is that n times p is greater than 5, and n times q is greater than 5.

01:21 So for this example, we have that n is 250, x is 110.

01:32 And we got that because 250 people were randomly surveyed, and 110's if they had a savings account.

01:40 So to do n times p, this would be, p would be 110 over 250, which is 0 .44.

01:51 Q is 1 minus 0 .44, which is 0 .56.

01:58 So 250 times 0 .44 is 110, and two fifty times point five six is one hundred and forty so both of them are greater than five so the we checked the assumptions there and we can move on to step three step three let's describe the sample evidence so we have a sample size of 250 we know that 110 of those 250 surveyed, have a savings account.

02:39 We're going to find p prime would be 110 over 250, because we're going to use p to estimate our sample evidence of p prime, which would be 0 .44.

02:53 Step four, let's calculate the confidence interval.

02:57 So remember, we were looking for a 95 % confidence interval.

03:01 So the first thing we want to find is the confidence coefficient...

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