Solution verification for hypothesis testing and confidence interval problemThere's a random sample of size&nbsp;n=10&nbsp;observations over a normally distributed population with standard deviation&nbsp;σ=2:8.7, 7, 4, 7.6, 3, 8.1, 6.4, 6.1, 9.4, 6.2- Find 96% confidence interval for the population mean- Test the hypothesis&nbsp;H0:μ=7.5&nbsp;against Ha:&nbsp;μ≠7.5&nbsp;with significance level&nbsp;α=0.01. Find approximation of the observed p value.My Solution:We are looking for real numbers l and u s.t.:P(l&lt;θ^&lt;u)=0.96, where&nbsp;θ^=∑i=1nXi−nθnσ2∼N(0,1)We are looking for&nbsp;z0.2&nbsp;which from the z-score table is: 2.055. Therefore:-2.055&lt;∑i=1nXi-nθnσ2&lt;2.055≡-2.05540&lt;∑i=1nXi-nθ&lt;2.05540≡≡12.996-66.5&lt;-10θ&lt;12.996-66.5≡5.350&lt;θ&lt;7.94.For the second part:We set two z-scores:&nbsp;z1=−2.325&nbsp;and&nbsp;z2=2.325&nbsp;from which we construct a two-tailed test.Our test statistic is:&nbsp;t=(6.65−7.5)102=−1.343⇒t≥−2.235&nbsp;from where we see the test statistic t is not in the rejection region, therefore we fail to reject the null hypothesis.

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Solution verification for hypothesis testing and confidence interval problemThere&#039;s a random sample of size&amp;nbsp;n=10&amp;nbsp;observations over a normally distributed population with standard deviation&amp;nbsp;σ=2:8.7, 7, 4, 7.6, 3, 8.1, 6.4, 6.1, 9.4, 6.2- Find 96% confidence interval for the population mean- Test the hypothesis&amp;nbsp;H0:μ=7.5&amp;nbsp;against Ha:&amp;nbsp;μ≠7.5&amp;nbsp;with significance level&amp;nbsp;α=0.01. Find approximation of the observed p value.My Solution:We are looking for real numbers l and u s.t.:P(l&amp;lt;θ^&amp;lt;u)=0.96, where&amp;nbsp;θ^=∑i=1nXi−nθnσ2∼N(0,1)We are looking for&amp;nbsp;z0.2&amp;nbsp;which from the z-score table is: 2.055. Therefore:-2.055&amp;lt;∑i=1nXi-nθnσ2&amp;lt;2.055≡-2.05540&amp;lt;∑i=1nXi-nθ&amp;lt;2.05540≡≡­12.996-66.5&amp;lt;-10θ&amp;lt;12.996-66.5≡5.350&amp;lt;θ&amp;lt;7.94.For the second part:We set two z-scores:&amp;nbsp;z1=−2.325&amp;nbsp;and&amp;nbsp;z2=2.325&amp;nbsp;from which we construct a two-tailed test.Our test statistic is:&amp;nbsp;t=(6.65−7.5)102=−1.343⇒t≥−2.235&amp;nbsp;from where we see the test statistic t is not in the rejection region, therefore we fail to reject the null hypothesis.

Gianna Travis · Accepted Answer

In first part of solution we must receive for duplex confidence interwal quantile:&amp;nbsp;zα:ϕ(α)=1−α2.To second of part use program R&amp;gt;data&amp;lt;−c(8.7,7.0,4.0,7.6,3.0,8.1,6.4,6.1,9.4,6.2)&amp;gt;X10=mean(data)&amp;gt;X10[1] 6.65&amp;gt;u10=6.65−7.5210&amp;gt;u10[1]−1.343968&amp;gt;1−0.012[1]0.995&amp;gt;k=q‖0.995‖&amp;gt;k[1]2.575829Value of statisticu10=-1,34∉(-∞,-2,58&amp;gt;∪&amp;lt;2,58,∞)There are no reasons to reject&amp;nbsp;H0&amp;nbsp;and to receive&amp;nbsp;H1.

Solution verification for hypothesis testing and confidence interval problem There's a random sa

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