The mock final

◈ 9 cards

Four worksheets and two written answers in the paper’s register, with no scaffolding: a t-interval, a two-proportion test, a binomial tail, a slope test with a bracketed p, then a one-sample t at the ∞ row and a two-proportion test with the meaning of its p-value.

Instructions

This is the final in miniature. Sit it the way the real one is sat: the $z$ -table (cumulative), the $t$ -table (upper-tail critical values, rows 1–30 and ∞), your one-page sheet from L14.3, and a calculator that does not do statistics. Budget about 1.5 minutes per mark; the four worksheets are worth roughly three marks each and the two written answers five each — 22 marks, 33 minutes. No lesson is named beside any item; deciding which lesson it is is the first mark of each.

Before you begin, the habits that lose marks when they slip:

Write the parameter line first — parameter, estimator, distribution with df. It is a mark on its own and it fixes the table.
Round $z$ to two decimals before the cumulative table; bracket a $t$ $p$ -value from its row, doubled if two-sided.
df above 30 → the ∞ row. Do not stop at row 30.
The test’s SE for a proportion uses $p_{0}$ (one sample) or the pooled $\overset{p}{^}_{c}$ (two samples); the interval’s uses $\overset{p}{^}$ .
The conclusion names the parameter, the direction, the context and $α$ , and says reject or do not reject — never accept, never prove.
A $p$ -value is a probability about the data if $H_{0}$ were true, not the probability that $H_{0}$ is true, and not the probability of being wrong.

The set

Worksheet 1. A sample of 25 invoices has mean processing time 18.6 days with $s = 4.2$ . Build the 95 % interval for the mean. ( $t_{0.025; 24} = 2.064$ .)

Worksheet 2. Region A: 30 defaults in 150 loans. Region B: 18 in 150. Compute the pooled proportion, $z$ , and the two-sided $p$ -value.

Worksheet 3. Each of 8 independent audits flags an issue with probability 0.25. Find $P (at least 2 flags)$ .

Worksheet 4. A regression on 14 points gives $\hat{β}_{1} = 3.42$ with $S E = 1.15$ . Compute $t$ and bracket the two-sided $p$ . (Row 12: 2.681 at 0.01, 3.055 at 0.005.)

Written 1. A firm claims its mean invoice-processing time is under 12 days. A sample of 36 gives $\overset{x}{ˉ} = 11.2$ , $s = 2.7$ . Test at 5 % by both routes and conclude for the CFO.

Written 2. The two regions of worksheet 2. Test at 5 % whether the default rates differ, and explain what your $p$ -value means to a credit manager.

After the set

Mark yourself against the rubrics with the same severity the paper uses: a right number with the wrong SE is the wrong number; a right decision with "accept $H_{0}$ " loses the conclusion mark; a $p$ -value described as "the chance the rates are the same" loses the interpretation mark. Then go back to the module whose lesson you could not name from the question — that, not the arithmetic, is what the final tests.