Question

A veterinarian's office recorded one particular week that they had 50 patients. The following table shows the recorded number of dogs.
Monday Tuesday Wednesday Thursday Friday

7 4 5 5 2


The formula for standard error is given below, where represents the sample proportion, and n is the total number of elements in the sample.




Use the given data to complete the table below.


Percentage of patients that were dogs [23%; 42%; 22%; 46%]

Standard error [.07; .09; .05; .16]

Margin of error 90% confidence interval [(32%, 60%)(34%,58%)(6%, 23%)(5%,21%)]

Margin of error 95% confidence interval [(32%, 60%)(34%,58%)(6%, 23%)(5%,21%)]

Answer 1

Answer:

1. The correct answer is 46%

2. The correct answer is .07

3. The correct answer is (34%,58%)

4. The correct answer is (32%,60%)

Step-by-step explanation:

1. Let's calculate the percentage or proportion of patients that were dogs:

p = (7 + 4 + 5 + 5 + 2)/50 = 23/50 = 0.46

The correct answer is 46%

2. Let's estimate the standard error, using the given formula, this way:

S.e = √ (0.46 * 0.54)/50 = √0.049 = 0.07

The correct answer is .07

3. Let's calculate the confidence limits of the 90% confidence interval, this way:

Confidence limits = proportion +/- 1.645 * standard error

Confidence limits = 0.46 +/- 1.645 * 0.07

Confidence limits = 0.46 +/- 0.12

Confidence limits = 0.34, 0.58

The correct answer is (34%,58%)

4. Let's calculate the confidence limits of the 95% confidence interval, this way:

Confidence limits = proportion +/- 1.96 * standard error

Confidence limits = 0.46 +/- 1.96 * 0.07

Confidence limits = 0.46 +/- 0.14

Confidence limits = 0.32, 0.60

The correct answer is (32%,60%)