A publisher reports that 38%38% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 340340 found that 32%32% of the readers owned a laptop. Find the value of the test statistic. Round your answer to two decimal places.

Question

Fury

Mathematics

12 January, 16:38

A publisher reports that 38%38% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 340340 found that 32%32% of the readers owned a laptop. Find the value of the test statistic. Round your answer to two decimal places.

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Answers (1)

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Litzy Fisher · Answer 1

Answer: - 0.71

Step-by-step explanation:

Let p = population proportion

po = sample proportion.

From the question,

p = 38% = 38/100 = 0.38

po = 32% = 32/100 = 0.32

Sample size (n) = 340.

Since our sample size is greater than 30 (n = 340) we will be making use of a z test for our test statistics.

The population standard deviation of the data set is given below as

σ = √p (1 - p).

σ = √0.38 (1 - 0.38)

σ = √0.38 * 0.62

σ = √0.2356

σ = 0.49.

Z score = po - p / (σ/√n)

Z score = 0.32 - 0.38 / (0.49/√340)

Z score = - 0.06 / 0.0266

Z score = - 0.71