Consider the Table Below Which Displays the Price of a Commodity

question 61

Essay

Consider the table below which displays the price of a commodity for six consecutive years.
$\begin{array}{c|c}\hline \text { Year } & \text { Price (dollars) } \\\hline 1 & 250 \\\hline 2 & 255 \\\hline 3 & 253 \\\hline 4 & 255 \\\hline 5 & 259 \\\hline 6 & 261 \\\hline\end{array}$

a. Use the method of least squares to fit the model $E \left( Y _ { t } \right) = \beta _ { 0 } + \beta _ { 1 } t$ to the data. Write the prediction equation.
b. Use the prediction equation to obtain forecasts of the prices in years 7 and 8 .
c. Find $95 \%$ prediction intervals for years 7 and 8 .

Understand the concept of standard error in the context of estimating proportions.

Calculate confidence intervals for population proportions.

Conduct hypothesis testing for population proportions.

Understand the effect of sample size on the power of a test and the accuracy of estimations.

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Definitions:

Confidence Interval

A range of values derived from sample data that is likely to contain the value of an unknown population parameter, with a certain level of confidence.

Retained Students

Students who have not progressed to the next academic grade or level as expected, often due to academic or other challenges.

Significance Level

A threshold for determining the probability of rejecting the null hypothesis in a statistical test, typically set before the data is collected.

Sample Data

A subset of data collected from a larger population, used for statistical analysis.