For problem 1 to 7, (a) identity the claim and state H_0 and H_a, (b) determine

Question

For problem 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 fall 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_2;alpha = 0.01. Sample Statistics: x_1, = 6, n_2 = 20 and x_2 = 4, n_2 = 30.

Explanation / Answer

H0: Median hourly wage of podiatrists is at least $55.89 ( Median >= 55.89 )
Ha: Median hourly wage of podiatrists is less than $55.89 ( Median < 55.89 )

Let level of significance is = 0.05, now by using following table for sign test we can write Z/2 = 5 for n = 23

Now critical value = 5.

Let there are 17 values which are less than $55.89 so number of negative signs( - ) would be 17, and 5 values are greater than $55.89 so number of plus signs ( + ) is 5.

Let x be the smaller number between ( + ) signs and ( - ), so x = 5,

Now the rejection croteria for this test is, reject H0 if x is less than the critical value,

Here x = 7 is greater than Z/2 = 5 so we fail to reject the null hypothesis, hence there is enough evidence that median hourly wage of podiatrists is may be at least $55.89

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