Weeks 8–10 · Confidence Intervals, Hypothesis Testing, Chi-Squared Tests
A sample of 64 invoices has a mean processing time of 14 days. The population standard deviation is 4 days. What is the standard error?
Using the same sample (n = 64, mean = 14, σ = 4), what is the upper limit of a 95% confidence interval? Round to 2 d.p.
Which gives a wider confidence interval — 90% or 99% confidence?
A firm claims average delivery time is 10 days. You sample 49 deliveries and get a mean of 11.2 days (σ = 3.5). What is the z test statistic?
Two-tailed test, α = 0.05, critical values ±1.96. Your z = 2.4. Do you reject H₀?
Your p-value is 0.03 and α = 0.01. Do you reject H₀?
A store claims equal sales across 3 products. In 120 sales:
| Product | A | B | C |
|---|---|---|---|
| Observed | 50 | 42 | 28 |
What is the expected frequency for each product?
Using the data from Q7, what is the chi-squared test statistic?
Consider this contingency table:
| Pass | Fail | Total | |
|---|---|---|---|
| Morning | 30 | 20 | 50 |
| Evening | 40 | 10 | 50 |
| Total | 70 | 30 | 100 |
What is the expected frequency for the Morning–Pass cell?
How many degrees of freedom does a 3 × 4 contingency table have?
Your χ² statistic is 10.3 and the critical value is 9.488. Do you reject H₀?
A goodness-of-fit test has 5 categories. What are the degrees of freedom?