Question

. In the USA the maximum acceptable level for exposure to microwave radiation is 10 μW/cm2 (microwatts per square centimetre). It is feared that a large TV transmitter may have raised the level of ambient microwave radiation above this level. Fourteen widely-spaced monitoring sites were selected among homes at roughly equal distances from the transmitter. For these sites, the mean radiation level was 10.95 μW/cm2 , with a standard deviation of 1.24 μW/cm2 .

(a) Do these results indicate that microwave radiation exposure is at an unacceptable level? Conduct an appropriate hypothesis test using α = 1%.

(b) If you were a parent with young children and you lived near the transmitter, would you want the significance level of the test to be 1% or 5%? Justify your answer. What significance level would you want if you were the owner of the transmitter?

(c) Provide a 90% confidence interval for the mean microwave radiation at this distance from the transmitter.

Answer 1

Answer a)

Step 1: Set up null and alternative hypotheses

H0: μ = 10
H1: μ > 10

Step 2: Calculate test statistic

x̅ (sample mean) = 10.95
n (sample size) = 14
s = (sample standard deviation) = 1.24

Test Statistic = (x̅ - μ)/(σ/√n) = (10.95-10)/(1.24/sqrt(14))

Test Statistic = 2.8666

Step 3: Compute p-value

Using the test statistic in Step 2 as a t-score, we will find the right-tailed area corresponding to this t-score.

Degrees of freedom = n-1 = 14-1 = 13

P-value is obtained using P-value calculator for t = 2.8666 and df = 13

P-value = 0.0066

Step 4: Decision

Since p-value = 0.0066 < α = 0.01, we reject null hypothesis.

Step 5:

At 0.01 significance level, there is sufficient evidence to indicate that microwave radiation exposure is at an unacceptable level

Answer b)

A parent with young children who lived near the transmitter, would want the significance level of the test to be 5%. This is because higher alpha value decreases the chance of committing Type II error. Type II error in this case is probability of concluding that microwave radiation exposure is acceptable, even when it is actually at an unacceptable level.

Answer c)

A 90% confidence interval for the mean microwave radiation at this distance from the transmitter is (10.363, 11.537)