1. The appropriate hypotheses are H0: μ ≤ 4.0, HA: μ > 4.0
2. The value of the test statistic is t = 2.40.
3. At a 5% significance level, the decision is to A. reject H0; we can conclude that the mean concentration of radon gas is greater than the safe level.
1. Hypotheses:
The null hypothesis (H0) states that the average level of radon gas is less than or equal to the safe level. The alternative hypothesis (HA) states that the average level of radon gas is greater than the safe level. Therefore, the appropriate hypotheses are:
H0: μ ≤ 4.0, HA: μ > 4.0
2. Test statistic:
We will use a one-tailed t-test because the alternative hypothesis is one-sided. The test statistic is calculated as:
t = (x - μ) / (s / √n)
where:
x = sample mean (4.4 pCi/L)
μ = hypothesized population mean (4.0 pCi/L)
s = sample standard deviation (1 pCi/L)
n = sample size (36 days)
Plugging in the values, we get:
t = (4.4 - 4.0) / (1 / √36) = 2.40
Therefore, the value of the test statistic is t = 2.40.
3. Decision:
At a 5% significance level, we need to compare the test statistic (t = 2.40) to the critical value from the t-distribution table with degrees of freedom (df) equal to n - 1 (36 - 1 = 35). Since the alternative hypothesis is one-tailed, we look up the critical value for a one-tailed test with 35 degrees of freedom and a significance level of 0.05.
The critical value is approximately 1.697.
Since the test statistic (2.40) is greater than the critical value (1.697), we reject the null hypothesis (H0).
Conclusion:
Therefore, there is sufficient evidence to conclude that the mean concentration of radon gas in the classroom is greater than the safe level of 4 pCi/L.
Final answer:
A. reject H0; we can conclude that the mean concentration of radon gas is greater than the safe level.
Question
A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L.
To test whether the average level of radon gas is greater than the safe level, the appropriate hypotheses are ________.
H0: μ ≤ 4.0, HA: μ > 4.0
H0: μ = 4.0, HA: μ ≠ 4.0
H0: μ ≥ 4.4, HA: μ < 4.4
H0: X = 4.4, HA: X ≠ 4.4
The value of the test statistic is ________.
t = –2.40
z = –2.40
t = 2.40
z = 2.40
At a 5% significance level, the decision is to ________.
A. reject H0; we can conclude that the mean concentration of radon gas is greater than the safe level
B. reject H0; we cannot conclude that the mean concentration of radon gas is greater than the safe level
C. not reject H0; we can conclude that the mean concentration of radon gas is greater than the safe level
D. not reject H0; we cannot conclude that the mean concentration of radon gas is greater than the safe level