---
title: "Test of proportion: 60 Minutes TV share"
subject: "Probability and Statistics"
chapter: 7
key: "semester_5/probability_and_statistics:tv-60-minutes-share-test"
source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/tv-60-minutes-share-test
site: BCT Engineering
---

# Test of proportion: 60 Minutes TV share

Probability and Statistics · Chapter 7: Inference concerning proportion

- Asked in: 2075 Chaitra, 5 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/tv-60-minutes-share-test
- Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-7

## Question

A simple random sample of Household with TV set in use. Show that 1024 of them were tuned to 60 minute while 3836 were tuned to some other show. Use 0.05 significant level to test the claim of CBS executive that "60 minute get more than a 20 share", which mean that more than 20% of set in use are tuned to 60 minute.

## Short answer

Test H0: p=0.20 vs H1: p>0.20. Sample n=4860, p̂=1024/4860≈0.2107, SE=√(0.2×0.8/4860)≈0.00574, z=1.865. Critical value 1.645 at 5%; reject H0, evidence supports more than 20% share.

## Answer

This is a right-tailed test of a single proportion (large sample).

```text
n = 1024 + 3836 = 4860,  x = 1024
p̂ = 1024/4860 = 0.2107,  p₀ = 0.20, q₀ = 0.80
```

1. H0: p = 0.20 (the share is 20%)
   H1: p > 0.20 (the CBS claim: more than 20% of sets are tuned to 60 Minutes)
2. Level of significance: α = 0.05
3. Test statistic:

```text
SE = √(p₀q₀/n) = √(0.20×0.80/4860) = 0.00574
z  = (p̂ − p₀)/SE = (0.2107 − 0.20)/0.00574 = 1.865
```

4. Critical value: z(0.05, right-tail) = 1.645. Reject H0 if z > 1.645.
5. Decision: z = 1.865 > 1.645 (p-value = 0.031), so **reject H0**.

**Conclusion:** at the 5% level there is sufficient evidence to support the CBS executive's claim that 60 Minutes gets more than a 20% share.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The claim is 'more than 20%'. What is H1?
   A. p < 0.20
   B. p ≠ 0.20
   C. p > 0.20 (right-tailed)
   D. p = 0.20
   Answer: C. A 'more than' claim is placed in H1, giving a right-tailed test. (Key point: Hypotheses)

2. What is n and p̂?
   A. n = 1024, p̂ = 1
   B. n = 4860, p̂ = 0.20
   C. n = 3836, p̂ = 0.79
   D. n = 4860, p̂ = 0.2107
   Answer: D. n = 1024 + 3836 = 4860 and p̂ = 1024/4860 = 0.2107. (Key point: Sample size)

3. What is the right-tail critical value at 0.05?
   A. 1.645
   B. 2.326
   C. 1.96
   D. 2.576
   Answer: A. z(0.05, right) = 1.645. (Key point: Critical value)

4. z = 1.865. What is concluded?
   A. Fail to reject H0
   B. Reject H0; evidence supports the claim
   C. Test is two-tailed
   D. Claim is false
   Answer: B. 1.865 > 1.645, so there is enough evidence for a share above 20%. (Key point: Decision)

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