Question

Use the following information for the next four (4) questions Suppose you work for the Las Vegas Chamber of Commerce, and you want to with 95% confidence, the difference between the percentage of all females who have gone to see an Elvis impersonator and the percentage of all impersonator. A random sample of 100 females includes 53 females who have seen an Elvis impersonator. A random sample of 110 males includes 37 males who have seen an Elvis impersonator estimate males who have gone to see an Elvis 41. For a 95% confidence interval, the z value is (a) 1.96 (b) 1.645 (c) 0.92 (d) 0.65 42. The difference between the sample proportions (females - males) is (a) 1.086 (b) 0.194 (c) 0.211 (d) 0.332

Answer 1

Solution:-

P_Female = 53/100 = 0.53

P_Male = 37/110 = 0.3364

41) The z_alpha/2 value for the 95% confidence interval is 1.96.

42) b) The difference between the sample proportion is 0.194

Difference = P_Female - PMale

Difference = 0.1936

43) The margin of error is

$M.E = z_{\alpha /2}\times \sqrt{\frac{p_{1}(1-p_{1})}{n_{1}}+\frac{p_{2}(1-p_{2})}{n_{2}}}$

M.E = 1.96 × 0.06723

M.E = 0.1318

44)

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

Null hypothesis: P₁ = P₂
Alternative hypothesis: P₁ ≠ P₂

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.

Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p = (p₁ * n₁ + p₂ * n₂) / (n₁ + n₂)

p = 0.4286

SE = sqrt{ p * ( 1 - p ) * [ (1/n₁) + (1/n₂) ] }
SE = 0.06838

z = (p₁ - p₂) / SE

z = 2.83

where p₁ is the sample proportion in sample 1, where p₂ is the sample proportion in sample 2, n₁ is the size of sample 1, and n₂ is the size of sample 2.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 2.83 or greater than 2.83

Thus, the P-value = 0.0046

Interpret results. Since the P-value (0.0046) is less than the significance level (0.05), we cannot accept the null hypothesis.

c) H₀ is rejected, there is difference in proportions.