A Simple Random Sample of Ten Firms Was Asked How

question 67

Essay

A simple random sample of ten firms was asked how much money (in thousands of dollars) they spent on employee training programs this year and how much they plan to spend on these programs next year. The data are shown below. $$\begin{array} { l r r r r r r r r r r } \text { Firm } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\text { This year } & 25 & 31 & 12 & 15 & 21 & 36 & 18 & 5 & 9 & 17 \\\text { Next year } & 21 & 30 & 18 & 20 & 22 & 36 & 20 & 10 & 8 & 15\end{array}$$ Assume that the populations of amount spent on employee training programs are normally distributed.
Can we infer at the 5% significance level that more money will be spent on employee training programs next year than this year?

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Definitions:

Critical Values

Thresholds or boundaries in statistical tests that define the region where the null hypothesis can either be rejected or not rejected.

National Survey

A large-scale survey conducted across a nation to collect various data from a representative sample of its population.

Test Statistic

A test statistic is a standardized value calculated from sample data during a hypothesis test. It's compared to a critical value to decide whether to reject the null hypothesis.

Age Distribution

A representation of the proportion of individuals of different ages within a specific population.