1. A random sample of 45 door-to-door encyclopedia salespersons were asked how l

Question

1. A random sample of 45 door-to-door encyclopedia salespersons were asked how long on average they were able to talk to the potential customer. Their answers revealed a mean of 8.5 minutes with a variance of 9 minutes. Construct a 95% confidence interval for , the time it takes an encyclopedia salesperson to talk to a potential customer.

2. It is believed that 70% of all TV households would be tuned in to Game 6 of the 1997 NBA Championship series between the Chicago Bulls and the Utah Jazz. A random sample of 500 TV households was selected and 365 indicated they were tuned into the game.

Find a 99% confidence interval for the true proportion of TV households tuned in to the game.

Explanation / Answer

Solution:-

1) Given that n = 45 , x = 8.5 ,variance = 9 .sd = 3 ,Z = 1.96

95% confidence iterval: X +/- (sd/sqrtn)

=> 8.5 +/- 1.96 * (3/sqrt(45))

(7.6234 , 9.3765)

2) Given that x = 365,n = 500
p = 365/500 = 0.73

99% confidence interval = p +/- Z sqrt(pq/n)
= 0.73 +/- 2.575*sqrt(0.73*0.27/500)
= (0.6788, 0.7811)
  

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