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# 1. Interstate Batteries guarantees its lawn tractor battery will last at least 3 years. To increase sales, the company plans to offer a new replacement warranty, as long as 95% of all batteries do indeed last at least 3 years. A random sample of 200 customers was contacted, and 183 had batteries that lasted at least 3 years. Is there evidence to suggest the proportion of tractor batteries that last at least 3 years is less than 95%?

(i) The null and alternative hypotheses are (use symbols)

Ho:_____________________________________ Ha: ________________________________________

(ii) the test value (test statistics) is:

___________________________________________________________

___________________________________________________________

(iii) At 5%, the critical value from the tables will be:

(a) 1.645

(b) - 1.645

(c) 1.96

(d) - 1.96

(e) 1.28

(iv) At the 5% level, the statistical conclusion will be

(a) Accept Ho, since _______________________________________________________

(b) Reject Ho, since _______________________________________________________

(v) The word conclusion will be

(a) Accept Ho, the proportion of tractor batteries lasting at least 3 years is 95%.

(b) Accept Ho, there is not enough evidence to say the proportion of tractor batteries lasting at least 3 years is less tha 95%.

(c) Reject Ho, the proportion of tractor batteries lasting at least 3 years is less than 95%.

(d) Reject Ho, the proportion of tractor batteries lasting at least 3 years is 95%.

(vi) Interpreting the results of the test: Interstate Batteries will be able to offer the new replacement warranty

YES

NO