Question

A poll surveyed 341 video gamers, and113 of them said that they prefer playing games on a console, rather than a computer or hand-held device. An executive at a game console manufacturing company claims that more than 28% of gamers prefer consoles. Does the poll provide convincing evidence that the claim is true? Use the α=0.10 level of significance and the P-value method with the Cumulative Normal Distribution Table. (a) State the appropriate null and alternate hypotheses. (b) Compute the value of the test statistic. Round the answer to at least three decimal places. (c)Determine whether to reject H0.

Answer 1

A)

Null hypothesis Ho : P = 0.28

Alternate hypothesis Ha : P > 0.28

B)

N = 341

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 95.48

N*(1-p) = 245.52

Both the conditions are met so we can use standard normal z table to estimate the P-Value

Test statistics z = (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed P = 113/341

Claimed P = 0.28

N = 341

After substitution

Test statistics z = 2.113

C)

From z table, P(z>2.11) = 0.0174

P-value = 0.0174

As 0.0174 < 0.1 (given significance)

We reject the null hypothesis Ho.