A marketing manager for a cell phone company claims that more than 55% of children aged 8-12 have cell phones. In a survery of 802 children aged 8-12 by the National Consumers League, 449 of them had cell phones. Can you conclude that the managers claim is true? Use the 0.01 level of signifance.

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Asked Jul 22, 2019
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A marketing manager for a cell phone company claims that more than 55% of children aged 8-12 have cell phones. In a survery of 802 children aged 8-12 by the National Consumers League, 449 of them had cell phones. Can you conclude that the managers claim is true? Use the 0.01 level of signifance. 

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Expert Answer

Step 1

Null and alternative hypotheses:

Here, to check whether more than 55% of children aged 8-12 have cell phones, the appropriate test is z-test for single sample proportion.

The hypotheses for the test is given below.

Null hypothesis:

H0: p0 = 0.55

Alternative hypothesis:

H1: p0 > 0.55

Sample proportion:

The sample proportion is calculated as follows.

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449 802 = 0.5599

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Step 2

Computation of test statistic:

The test statistic for z-test for single sample proportion is as follows.

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P Po Po(1-Po) n

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Step 3

Calculations:

Here, n = 802.

The sample proportion, p = 0.5599.

The population proportion, p0 = 0.55.

The value of test stat...

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0.5599 0.55 0.55(1-0.55 802 0.0099 0.0176 =0.563

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