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A study found that, in 2005, 12.5% of U.S. workers belonged to unions (The Wall Street Journal, January 21, 2006). Suppose a sample of 420 U.S. workers is collected in 2006 to determine whether union efforts to organize have increased union membership. Formulate the hypotheses that can be used to determine whether union membership increased in 2006. H0: p Ha: p If the sample results show that 52 of the workers belonged to unions, what is the sample proportion of workers belonging to unions (to 2 decimals)? 0.12 Complete the following, assuming an level of .05. Compute the value of the test statistic (to 2 decimals). What is the p-value (to 4 decimals)? What is your conclusion?

Respuesta :

Answer:

a. The value of Sample proportion(p) = 52 ÷ 420 = 0.124 ≈ 0.12

The formula for computing the test statistic is given by,

z = (p - P) ÷ σ

where, p is the sample proportion = 0.12

P is the hypothesized value of Population Proportion = 12.5% = 0.125

and σ is standard deviation

σ = [tex]\sqrt{\frac{P(1-P)}{n}}[/tex]

⇒ σ = 0.01

Putting all value in z. We get,

z = (0.12 - 0.125) ÷ 0.01

⇒ z = -0.5

Thus, the p-value at 5% level of significance foe one-tail test = 0.3085

Thus, we reject the null-hypothesis. Since, z-value > p-value.

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