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M3ex4 T-Test

The document presents a statistical analysis of the lifetime of electric bulbs based on a sample of 10 bulbs. For a hypothesized mean of 4, the sample mean did not show a significant difference, while for a hypothesized mean of 6, the sample mean differed significantly. The analysis includes test statistics and p-values for both hypotheses.

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7 views2 pages

M3ex4 T-Test

The document presents a statistical analysis of the lifetime of electric bulbs based on a sample of 10 bulbs. For a hypothesized mean of 4, the sample mean did not show a significant difference, while for a hypothesized mean of 6, the sample mean differed significantly. The analysis includes test statistics and p-values for both hypotheses.

Uploaded by

dvsh0429
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Name: Divesh Pradhan

Roll no: 2526-1195-31


Date: 8/24/2025
Sub: Statistics

Q)

The lifetime of electric bulbs for a


random sample of 10 from a large consignment gave the following data:
Item 1 2 3 4 5 6 7 8 9 10

Life
in ‘000 hrs 4.2 4.6 3.9 4.1 5.2 3.8 3.9 4.3 4.4 5.6

Can we accept the hypothesis that there


is no significant difference in the sample mean and the hypothetical population
mean, μ=4.

(2nd part
– if hypothetical population mean, μ=6)
Sample Data (in 000 hours)
[4.2, 4.6, 3.9, 4.1, 5.2, 3.8, 3.9, 4.3, 4.4, 5.6]

Sample Statistics
Sample size (n) = 10

Sample mean (x̄) = 4.40

Sample standard deviation (s) = 0.589

Degrees of freedom (df) = 9

Part 1: Hypothesized Mean μ = 4


H₀: μ = 4 (no significant difference)
H₁: μ ≠ 4 (significant difference)

Test statistic: t = 2.148

p-value = 0.0602

Decision: At α = 0.05, Fail to reject H₀. (Conclusion: The sample mean does not differ
significantly from 4.)

Part 2: Hypothesized Mean μ = 6


H₀: μ = 6 (no significant difference)
H₁: μ ≠ 6 (significant difference)

Test statistic: t = -8.593

p-value = 0.000012

Decision: At α = 0.05, Reject H₀. (Conclusion: The sample mean differs significantly
from 6.)

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