Directions: For problems 1 to 7, (a) identity the claim and state H_o and H_a, (

Question

Directions: For problems 1 to 7, (a) identity the claim and state H_o and H_a, (b) critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject then hypothesis, and (e) interpret the decision in the context of the original claim. A labor organization estimates that the median hourly wage of podiatrists is at least $55.89. In a random sample of 23 podiatrists, 17 are paid less than $55.89 per hour, 5 are paid more than $55.89 per hour, and 1is paid $s5.89 per hour. At alpha = 0.05, can you reject the labor organization's claim? A pet association claims that the mean annual cost of routine veterinarian visits for dogs and cats are the same. The results for samples of the two types of pets are shown below. At alpha = 0.10, can you reject the pet association's claim? Assume the population variance are not equal. The lengths of time (in years) it took a random sample of 32 former smokers to quit smoking permanently are listed. At alpha =0.05, is there enough evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 15 years? A medical researcher says that less than 25% of US adults are smokers. In a random sample of 200 US adults, 18.5% say that they are smokers. At alpha =0.05, is there enough evident to reject the researcher's claim? Claim: mu=15; alpha= 0.01. Sample statistics: x^bar=13.9, s=3.23, n=6. Claim: mu_d > 0; alpha=0.05. Statistics: d^bar=0.55, s_d=0.99, n=28. Claim: p_1 > p_2: alpha =0.01. Sample Statistics: x_1=6, n_1=20 and x_2=4, n_2=30.

Explanation / Answer

Solution:-

7)

p1 = 0.3

p2 = 0.1333

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 one-tailed test. The null hypothesis will be rejected if the proportion of women catching cold (p1) is sufficiently smaller than the proportion of men catching cold (p2).

Formulate an analysis plan. For this analysis, the significance level is 0.01. 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 = 0.2

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

SE = 0.1155

z = (p1 - p2) / SE

z = 1.44

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 one-tailed test, the P-value is the probability that the z-score is less than 1.44. We use the Normal Distribution Calculator to find P(z > 1.44) = 0.075

Interpret results. Since the P-value (0.075) is greater than the significance level (0.01), we cannot reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that P1 > P2.

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