Question

In a study of cell phone usage and brain hemispheric​ dominance, an Internet survey was​ e-mailed to 6978 subjects randomly selected from an online group involved with ears. There were 1314 surveys returned. Use a 0.01 significance level to test the claim that the return rate is less than​ 20%. Use the​ P-value method and use the normal distribution as an approximation to the binomial distribution.

Identify the null hypothesis and alternative hypothesis. A. Upper H 0​: pequals0.2 Upper H 1​: pnot equals0.2 B. Upper H 0​: pless than0.2 Upper H 1​: pequals0.2 C. Upper H 0​: pgreater than0.2 Upper H 1​: pequals0.2 D. Upper H 0​: pequals0.2 Upper H 1​: pless than0.2 Your answer is correct.E. Upper H 0​: pnot equals0.2 Upper H 1​: pequals0.2 F. Upper H 0​: pequals0.2 Upper H 1​: pgreater than0.2

The test statistic is z = ​(Round to two decimal places as​needed.)

Answer 1

The null hypothesis is H0: p = 0.20, and the alternative hypothesis is H1: p < 0.20. The goal of the test is to determine if the return rate is less than 20%. The P-value method is used, with the normal distribution as an approximation to the binomial distribution.

Step-by-step explanation:

The null hypothesis is H0: p = 0.20, and the alternative hypothesis is H1: p < 0.20. The goal of the test is to determine if the return rate is less than 20%. The P-value method is used, with the normal distribution as an approximation to the binomial distribution.

To calculate the test statistic, we first need to find the standard error of the proportion. The formula for the standard error is:

SE = √[(p(1-p))/n]

In this case, p is the assumed population proportion, which is 0.20, and n is the sample size, which is 1314. Plugging in the values, we get:

SE = √[(0.20(1-0.20))/1314] ≈ 0.011

Next, we calculate the Z-score using the formula:

Z = (x - μ)/SE

Where x is the sample proportion, μ is the assumed population proportion (0.20), and SE is the standard error. Plugging in the values, we get:

Z = (0.1314 - 0.20)/0.011 ≈ -6.27

The test statistic is z = -6.27 (rounded to two decimal places).