Hypothesis Test of 1 Proportion 3, A new insectercide is advertized to kill more

Question

Hypothesis Test of 1 Proportion 3, A new insectercide is advertized to kill more than 95% of roaches on contact. The insectercide was applied to 400 roaches. Only 384 died immediately after contact. a. Is this sufficient evidence to support ther manufacturer's claim of 95%. Use -0.05 Level of significance. b. Find a 95% confidence interval for the true proportion of roaches killed on contact pa Test statistic Z= and Confidence Interval p±z- Po (1-po) State the null and alternative hypothesis State your conclusion for your hypothesis test Give the 95% Confidence Interval. Give a conclusion for the confidence interval test 4 points 4 points 4 points

Explanation / Answer

phat = 384/400 = 0.96

po = 0.95

n=400

alpha = 0.05

Hypothesis:

Ho : po = 0.95

Vs

H1 : po is not equals to 0.95

test statistic :

Z = (0.96-0.95) / sqrt{ (0.95*0.05) / 400 }

=

0.917663

P-value = 0.3588

P-value > alpha

So, we fail to reject null hypothesis.

Confidence interval according to given formula is (0.940796, 0.979204)

almost 95% of observations lie within the interval (0.940796, 0.979204)

0.917663

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