明天是DUE DATE了,我一点概念都没有的,用了一个多小时,刚刚做好两道题目,还有4道,我要完蛋了拉

A company that manufacutres batteries has developed a new battery that will hopefully have a much longer lifetime.  the company is about to embark on a new advertising campaign so wishes to estimate and test various assumptions abou this new technology beforehand.
Firstly they wish to investigate the ifetime of the new "long-life" batteries.  To do this, they randomly select 26 batteries and recond their lifetimes in a variety of different household appliances.  The summary of the data collected is displayed in the table below:

Lifetimes  of new long-life batteries (thousands of hours)
Mean                  4.342
Standard Error        0.179
Median                4.346
Mode                  N/A
Standard Deviation    0.915
Sample Variance       0.837
Count                 26

Q1. (You may round your answers to 3 decimal places.) It is assumed that battery lifetimes will follow a normal distribution.  Let μ1 be the mean lifetime of ALL batteries produced with this technology
i) Roughtly how large a sample would you need to estimate the mean lifetime to within 400 hours with 90% confidence? Is your sample size large enough?
ii) Estimate  μ1 with 90% confidence
iii) It is known from past experience that the mean lifetime of the previous batteries is 2000 hours.  They believe that their new "long-life" batteries will have on average, more than double this lifetime, but before using this claim in their advertising they wish to test this.  Test at the 10% significancee level whether there is statistical evidence that the new batteries have more than double the mean lifetime of the previous batteries.


These new batteries are more expensive to manufacturer, and will retail for 40% more than the company’s current economy brand on the market.  Before starting production, the company wishes to ascertain whether there would be a sufficient share of the market prepared to purchase them at the additional cost.  To do this, a random sample of 2040 potantial consumers are surveyed and asked whether they would condiser purchasing these batteries at the dearer price, given that they have, on average, more that twice the lifetime of their cheaper batteries.  Of those surveyed, 291 said that they would buy the new bbatteries.

Q2 (You may round your answers to 4 decimal places.) Let p1 be the proportion of ALL cousumers who would consider purchasing the new batteries.
i) How large a sample would be needed to estimate p1 to within 2% (ie 0.02) with 95% confidence? Is your sample size large enough?
ii) Estimate p1 with 95% confidence
iii) It is condiered that it would not be cost effective to market this product if the proportion of consumers prepared to try them is less than 15%.  See if there is statistical evidence to suggest that they should not market this product.  Test this at α=0.05
iv) Calculate the p-value of the test in part iii)
v) Using you p-value from part iv), now perform the above test with α=0.10