Question

In the past several years, many school districts in the state of Washington have experienced a shortage of qualified teachers to fill vacancies that have become available. A claim has been made that a possible reason for the shortage is that schools in Washington tend to pay teachers less on average than other schools in the United States. From data provided by the National Center for Education Statistics, you know that the average certified teacher in the United States earns an annual salary of $56,000. Based on a random sample of 70 certified teachers in Washington, you calculate the state’s mean salary as $53,000 with a standard deviation of $13,000.

1. Test the claim that the state average is different from the national average at the α = 0.05 significance level (Use a two-tailed test). What do you conclude?
2. Could you state the same result at the .01 and the .10 level of significance
3. Compute the p-value and interpret it.

Answer 1

(a) The hypothesis being tested is:

H₀: µ = 56,000

H_a: µ ≠ 56,000

56,000.00	hypothesized value
53,000.00	mean 1
13,000.00	std. dev.
1,553.80	std. error
70	n
69	df
-1.931	t
.0576	p-value (two-tailed)

The p-value is 0.0576.

Since the p-value (0.0576) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the state average is different from the national average.

(b) Since the p-value (0.0576) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the state average is different from the national average.

Since the p-value (0.0576) is less than the significance level (0.10), we can reject the null hypothesis.

Therefore, we can conclude that the state average is different from the national average.

(c) The p-value is 0.0576.

If H₀ is true, the probability of rejecting the null hypothesis is 0.0576.