Directions: For problems 1 to 7, (a) identity the claim and state H_0 and H_a, (
ID: 3218158 • Letter: D
Question
Directions: For problems 1 to 7, (a) identity the claim and state H_0 and H_a, (b) determine the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null 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 1 is paid $55.89 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 = 13.9, s = 3.23, n = 6. Claim: mu_d > 0; alpha = 0.05. Statistics: d = 0.55, s_d = 0.99, n = 28. Claim: p_1 > p_1; alpha = 0.01. Sample Statistics: x_1 = 6, n_1 = 20 and x_2 = 4, n_2 = 30.Explanation / Answer
Question 1
A]
Identify the claim and state H0 and Ha
Null hypothesis: H0: The median hourly wage of podiatrists is at least $55.89.
Alternative hypothesis: Ha: The median hourly wage of podiatrists is at less than $55.89.
H0: m 55.89 versus Ha: m < 55.89
B]
Determine the critical value
We are given a level of significance = alpha = 0.05
There will be two cells in the gof analysis. So, df = 1
So, by using Chi square table
Critical value = 3.84
C]
Find the test statistic
Chi square = [(O – E)^2/E]
The calculation table is given as below:
O
E
(O - E)^2/E
Less than 55.89
17
11
3.272727273
Greater than 55.89
5
11
3.272727273
Total
22
22
6.545454545
Chi square = [(O – E)^2/E] = 6.545454545
D]
Decision
We have
Test statistic value = Chi square = [(O – E)^2/E] = 6.545454545
Critical value = 3.84
Test statistic value > Critical value
So, we reject the null hypothesis that the median hourly wage of podiatrists is at least $55.89.
E]
Interpretation
From this test, we concluded or interpret that there is insufficient evidence that the median hourly wage of podiatrists is at least $55.89.
We can also interpret that there is sufficient evidence that the median hourly wage of podiatrists is at less than $55.89.
O
E
(O - E)^2/E
Less than 55.89
17
11
3.272727273
Greater than 55.89
5
11
3.272727273
Total
22
22
6.545454545
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