Question

This seems like to many cans to the company, so they test 100 and find that 62 have 12 oz or more. Construct a 90% confidence interval for the proportion of cans that have at least 12 oz of cola.

What is the margin of error for this interval? Round your answer to 4 decimal places.

What is the lower bound of this interval? Round your answer to 4 decimal places.

What is the upper bound of this interval? Round your answer to 4 decimal places

What parameter belongs to this interval?

		none of these
		please show work and excel work

Answer 1

Solution :

The 90% confidence interval for population proportion is given as follows :

Where, p̂ is sample proportion, q̂ = 1 - p̂, n is same size and Z_(0.10/2) is critical z-value to construct 95% confidence interval.

Note : The term after the plus minus sign is known as margin of error for the interval.

Sample proportion of cans that have at least 12 oz of cola is given by,

n = 100

Using Z-table we get, Z_(0.10/2) = 1.645

Hence, 90% confidence interval for the proportion of cans that have at least 12 oz of cola is,

The term after the plus minus sign is calculated to be 0.0798.

Hence, margin of error of the interval is 0.0798.

The lower bound of the interval is 0.5402.

The upper bound of the interval is 0.6998.

The population proportion of cans that have at least 12 oz of cola belongs to this interval.

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