Question

All parts please

1. A well-known brokerage firm executive claimed that at least 90% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 800 people, 88% of them said they are confident of meeting their goals.

a) State the null hypothesis as a complete sentence:

State the alternative hypothesis as a complete sentence:

How could we re-write the claim to make this a two-tail test?

b) What practical conclusion can we make about the claim?

c) How many people in the sample said they were confident of meeting their goals?

How many people were needed for this sample for 90% to have said they were confident of meeting their goals?

How many people would need to change their mind, how many people would need to go from saying they are not confident to saying they are confident, for 90% of the sample to say they are confident of meeting their goals?

Answer 1

a) Null hypothesis : Not more than 90% of investors are currently confident of meeting their investment goals.

Alternative hypothesis : At least 90% of investors are currently confident of meeting their investment goals.

To make this a two-tail test we can write claim as Investors currently confident of meeting their investment goals is different from 90 %.

b) Practical conclusion which can be made about the claim is that the market is good and investors are confident of investing enough money to reach their goal.

c) People in the sample said they were confident of meeting their goals = 0.88 * 800 = 704

People needed for this sample for 90% to have said they were confident of meeting their goals = 0.9 * 800 =720

People would need to change their mind = 720 - 704 = 16