Question

. 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 P = 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 α = 0.05.

Answer 1

a)

Hypothesis:

b)

np = 26*0.2 = 5.2

nq = 26*0.8 = 20.8

Both the Values are greater than 5, So we can use CLT

C)

sample proportion:

Test statistic:

C)

P-value: 0.9219 ...........Using standard normal table

Conclusion:

P-value > , i.e. 0.9219 > 0.05, That is Fail to Reject Ho at 5% level of significance.

Therefore, There is Not sufficient evidence to conclude that the population of all such panes, the probability the glass shatters under these conditions is different from P = 0.2