With domestic sources of building supplies running low several years ago, roughl

Question

With domestic sources of building supplies running low several years ago, roughly 60,000 homes were built with imported Chinese drywall. According to an article federal investigators identified a strong association between chemicals in the drywall and electrical problems, and there is also strong evidence of respiratory difficulties due to the emission of hydrogen sulfide gas. An extensive examination of 51 homes found that 40 had such problems. Suppose these 51 were randomly sampled from the population of all homes having Chinese drywall. (a) Does the data provide strong evidence for concluding that more than 50% of all homes with Chinese drywall have electrical/environmental problems? Carry out a test of hypotheses using alpha = 0.01. State the appropriate nu and alternative hypotheses. H_0: P = 0.5 H_a: p

Explanation / Answer

The statistical software output for this problem is:

One sample proportion hypothesis test:
p : Proportion of successes
H0 : p = 0.5
HA : p > 0.5

Hypothesis test results:

Hence,

z = 4.53

P - value = 0.0000

Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 41 50 0.82 0.070710678 4.5254834 <0.0001

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