Question

Level Estim Prob Hypoth Prob 0.60000 15 <40 0.40000 42 0.60000 > 40 0.40000 z Test Prob z Test Statistic -2.8868 0.0039 Frequencies Method: Fix hypothesized values, rescale o Level Count Prob Test Probabilities <40 20 0.40000 >40 Total N Missingo 2 Levels 30 0,60000 50 1.00000 Level Estim Prob Hypoth Prob <40 0.40000 0.30000 >40 0.60000 0.70000 z Test Prob z Test Statistic 1.5430 0.1228 Test Probabilities Method: Fix hypothesized values, rescale Level Estim Prob Hypoth Prob 0,50000 <40 0.40000 Test Probabilities 40 0.60000 0.50000 Level Estim Prob Hypoth Prob z Test Prob>z <40 0.40000 0.20000 Test Statistic -1.4142 0.1573 >40 0.60000 0.80000 Method: Fix hypothesized values, rescale omitted z Test Prob z Test Statistic 3.5355 0.0004 Method: Fix hypothesized values, rescale o Click here to access the JMP applet in a new window (a) Determine the hypothesis test to be done if the committee wants to see if the proportion of voters under 40 is different than the county average Ho: p 0.3 H1 p 0.3 Ho: u-0.3 H1: 0.3 Ho: p 0.3 H1: p0.3 Ho 0.7 H 0.3 Ho: p 0.3 H1: p 0.3 (b) Find the test statistic for the given hypothesis test. Also, find the critical value for a test with a = 0.1. (Round your answers to three decimal places.) test statistic critical value (c) Based on the test statistic and critical value, should the null hypothesis be accepted or rejected? The test statistic suggests we reject the null hypothesis; the proportion of voters younger than 40 is not statistically different in the town

Answer 1

Solution:-

a)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.30
Alternative hypothesis: P $\neq$ 0.30

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.10. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.06481
b)

z = (p - P) /S.D

z = 1.543

z_Critical = + 1.645

Rejection region is - 1.645 > z > 1.645

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Interpret results. Since the z-value (1.543) does not lies in the rejection region, hence we failed to reject the null hypothesis.

c) The test statistic suggests we accept the null hypothesis, the proportion of voters younger than 40 is not statistically different in the town.