An investigator computes a 95% confidence interval for a population mean on the basis of a sample of size 65. If she wishes to compute a 95% confidence interval that is half as wide, how large a sample does she need

The value is  

Step-by-step explanation:

From the question we are told the confidence level is  95% , hence the level of significance is    

=>  

Generally from the normal distribution table the critical value  of   is  

Generally the width of  a confidence interval is dependent on the margin of error which is mathematically represented as

Here is the standard deviation  

Let assume that and   are constant for the width of the confidence interval when the sample size is  n =65 and now that it has been divided to two

=>  

Here  K is a constant  

=>  

=>    

Now let be the margin of error and sample size before the reduction

  So

and let be the margin of error and sample size after the reduction  

    So  

=>  

=>  

=>  

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: