Answer to Question #198256 in Statistics and Probability for Mae

Question

The average price of 350 cellphones is ₱13,500 with the sample standard deviation of ₱750.

a. Find the 99% confidence interval of the true average price of the cellphones.

b. Find the length of the confidence interval.

Answer 1

Part (1)

The Confidence Interval formula is

$$\bar{X} ± Z \frac{s}{\sqrt{n}}$$

Where:

• X is the mean=13500
• Z is the Z-value from the table below=2.576
• s is the standard deviation=750
• n is the number of observations=350

Note:-

Z =2.576 for 99% confidence.

Put all value in formula and we get

$$13500 ± 2.576 \frac{750}{\sqrt{350}}$$

Now solve ,we get

Confidence interval=(13500 ± 103)

=(13397 to 13603)

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Part (2)

length of the confidence interval

= Upper value of interval - lower value of interval

=13603-13397

=206