Question

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 400 people, 16% 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 0.05 significance level. The null and alternative hypothesis would be: H 0 : p ≤ 0.2 H 1 : p > 0.2 H 0 : μ ≤ 0.2 H 1 : μ > 0.2 H 0 : μ ≥ 0.2 H 1 : μ < 0.2 H 0 : p = 0.2 H 1 : p ≠ 0.2 H 0 : μ = 0.2 H 1 : μ ≠ 0.2 H 0 : p ≥ 0.2 H 1 : p < 0.2 The test is: left-tailed right-tailed two-tailed The test statistic is: (to 3 decimals) The p-value is: (to 4 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothesis

Answer 1

H 0 : p ≥ 0.2

H1 : p < 0.2

Next part:

left-tailed

p-value< significance(alpha=0.05), reject the null hypothesis.

There is enough evidence to support the claim that the proportion of people who are confident is smaller than 20%