Question

3. A study is conducted regarding shatterproof glass used in automobiles. Twenty-six glass panes are coated with an anti-shattering film. Then a 5-pound metal ball is fired at 70mph at each pane. Five of the panes shatter. We wish to determine whether, in the population of all such panes, the probability the glass shatters under these conditions is different from = 0.2. (a) State the appropriate null and alternative hypotheses. (b) Check the conditions for trusting the conclusion of the test, and calculate the observed value of an appropriate test statistic. (c) Calculate the p-value. and draw a conclusion, given the significance level a= 0.05.

Answer 1

Answer:

Given that:

Twenty-six glass panes are coated with an anti-shattering film. Then a 5-pound metal ball is fired at 70mph at each pane. Five of the panes shatter.

a) State the appropriate null and alternative hypotheses

null Hypothesis: Но: 0.200 p alternate Hypothesis: Ha: 0.200

b) Check the conditions for trusting the conclusion of the test, and calculate the observed value of an appropriate test statistic.

for np and n(1-p) both are greater than or equal to 5 and sample is random, therefore condition is satisfied for normal approximation of binomial distribution

sample success 5 X sample size 26 =V(p*(1-p)/n) = std error Se 0.0784 x/n sample proportion p 0.1923 (p-p)/Se= test stat Z -0.10 LO

(c) Calculate the rejection region and draw a conclusion, given the significance level α= 0.05.

Decision rule: reject Ho if absolute value of test statistic z]>1.96

as test statistic does not falls in rejection region we can not reject null . We do not have evidence to conclude that probability the glass shatters under these conditions is different from π= 0.2