To prove they provide adequate protection against head injur…

To prove they provide adequate protection against head injuries, bicycle helmets must be able to withstand government impact tests without cracking more than 8% of the time. A new helmet design has just been introduced. The new helmet is thought to be more stylish than older helmets, but consumer groups are worried that it will crack more than 8% of the time.     300 of the new helmets are randomly sampled and tested. Of these sampled helmets, 29 of them cracked. Test the hypothesis that the new helmets will crack more than 8% time when enduring the impact tests. Assume independence. Use .05 as the level of significance.   Explain how each of the conditions of the Central Limit Theorem are met.

Suppose a random sample of 41 TI-84 calculators is taken to…

Suppose a random sample of 41 TI-84 calculators is taken to see what proportion has the Stat Wizards mode turned on. A 95% confidence interval for the population proportion of TI-84 calculators with Stat Wizards turned on turns out to be (.283, .388). If instead a new 95% confidence interval is calculated with a new sample size of 410 calculators, how would it differ from the 95% confidence interval?