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How could we re-write the claim to make this a two-tail test? Test the claim that the proportion of people who are confident is smaller than 90% at the 0.05 significance level. Determine the test statistic to three decimal places. Test the claim that the proportion of people who are confident is smaller than 90% at the 0.05 significance level. Determine the p-value to the fourth decimal place.

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Therefore, the p-value comes out to be 0.0296.

What is Confidence Interval?

A confidence interval is the range of approximations for an unknown variable in frequentist statistics. The most common confidence level for computing confidence intervals is 95%, however other levels, including 90% or 99%, are sporadically employed.

Here,

null and alternative hypothesis is,

null  hypothesis : p < 0.90

alternate hypothesis : p ≥ 0.90

a)

To make this hypothesis two tailed, statement should be

well-known brokerage firm executive claimed that  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.

b)

Here, test statistics is,

Z=[tex]\frac{p'-p}{\sqrt{p(1-p)/n} }[/tex]

 =(0.88-0.90)/√0.90×(1-0.90)/800

 =-1.886

c)

p-value is 0.0296

Therefore, the p-value comes out to be 0.0296.

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