IMathAS-libretexts

A well-known brokerage firm executive claimed that 20% 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 500 people, 14% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is smaller than 20% at the 0.025 significance level.

The null and alternative hypothesis would be:

\displaystyle {H}_{{0}}:{p}={0.2}

\displaystyle {H}_{{1}}:{p}≠{0.2}

\displaystyle {H}_{{0}}:{p}\le{0.2}

\displaystyle {H}_{{1}}:{p}>{0.2}

\displaystyle {H}_{{0}}:\mu={0.2}

\displaystyle {H}_{{1}}:\mu≠{0.2}

\displaystyle {H}_{{0}}:\mu\le{0.2}

\displaystyle {H}_{{1}}:\mu>{0.2}

\displaystyle {H}_{{0}}:\mu\ge{0.2}

\displaystyle {H}_{{1}}:\mu<{0.2}

\displaystyle {H}_{{0}}:{p}\ge{0.2}

\displaystyle {H}_{{1}}:{p}<{0.2}

The test is:

two-tailed

right-tailed

left-tailed

The test statistic is: (to 3 decimals)

The p-value is: (to 4 decimals)

Based on this we:

Fail to reject the null hypothesis
Reject the null hypothesis

License