A study is conducted regarding shatterproof glass used in automobiles. 26 glass

Question

A study is conducted regarding shatterproof glass used in automobiles. 26 glass panes were coated with an anti-shattering film; then a 5lb. metal ball was fired at 70mph at each of the glass panes. 5 of them fractured to the extent that they were considered shattered. We wish to determine whether the probability that the glass shatters under these conditions is different from .20.

(a) State the appropriate null and alternative hypotheses.

(b) Write down the test statistic, check the conditions for trusting the conclusion of the test, and calculate the observed value of the test statistic.

(c) Calculate the rejection region and decide the test if = .05.

(d) Calculate the p-value

Explanation / Answer

H0: p=0

Ha: p not equal to 0

Two tailed test

b) Sample size = 26

Sample proportion = 5/26 = 0.1923

We can conduct test assuming random sampling is assured and sample size 20 is good for the population.

p difference = 0.1923-0.20 = -0.0077

Variance p(1-p)/n = 0.2(0.8)/20

std error for p = 0.283

Hence t statistic = -0.0077/0.283 = -0.02722

p value = 0.978

p > 0.0t hence accept null hypothesis.

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