Data Analytics with Python Week 4 NPTEL Assignment Answers 2025

NPTEL Data Analytics with Python Week 4 Assignment Answers 2024.

1. If we have a sample size of 15 and the population standard deviation is known, we will use:

Options:
a) t-test for hypothesis testing
b) z-test for hypothesis testing
c) both t and z test
d) F Test

Answer: b
Explanation: When the population standard deviation is known, the z-test is used regardless of sample size. The t-test is used only when the population standard deviation is unknown and the sample size is small (n < 30).

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2. The quality-control manager at a Li-BATTERY factory needs to determine whether the mean life of a large shipment of Li-Battery is equal to the specified value of 375 hours. The process standard deviation is known to be 100 hours. A random sample of 64 batteries indicates a sample mean life of 350 hours. State the null hypotheses.

Options:
a) Mu = 375
b) Mu ≤ 375
c) Mu = 350
d) Mu ≥ 350

Answer: a
Explanation: The null hypothesis is a statement of no effect or no difference. In this case, we are testing whether the mean is equal to 375 hours, so the null hypothesis is Mu = 375.

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3. In question 3, At the alpha = 0.05 level of significance, is there any evidence that the mean life differs from 375 hours?

Options:
a) Yes, there is
b) No, there is not
c) None of the above

Answer: b
Explanation: Since the calculated p-value is greater than 0.05 (as given in question 5), we fail to reject the null hypothesis. Therefore, there is no sufficient evidence to say the mean life differs from 375 hours.

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4. In question 3, the computed p-value is:

Options:
a) 0.0456
b) 0.456
c) 0.0228
d) 0.228

Answer: a
Explanation: The z-test for this sample yields a z-score of -2.0 (using formula: z = (350 – 375)/(100/√64) = -2.0). The corresponding p-value for two-tailed test is 0.0456.

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5. In question 3, at a 95% confidence interval, the estimate of the population mean life of the battery is:

Options:
a) 325.5 to 379.5
b) 325.5 to 374.5
c) 320.5 to 379.5
d) 320.5 to 374.5

Answer: b
Explanation: CI = X̄ ± Z(σ/√n) = 350 ± 1.96(100/√64) = 350 ± 24.5 → [325.5, 374.5].

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6. The mean cost of a hotel room in a city is $168 per night. A random sample of 25 hotels resulted in X̄ = $172.50 and sample standard deviation s = 15.40. Calculate the t statistic.

Options:
a) 2
b) -2
c) 1.46
d) -1.46

Answer: c
Explanation: t = (X̄ – μ) / (s/√n) = (172.5 – 168)/(15.4/√25) = 4.5 / 3.08 ≈ 1.46.

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7. At the α = 0.05 level. In question 7, the decision on the null hypothesis is:

Options:
a) Do not reject
b) Reject
c) None of the above

Answer: a
Explanation: For df = 24, the critical t-value at α = 0.05 (two-tailed) is approximately ±2.064. Since 1.46 < 2.064, we do not reject the null hypothesis.

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8. In the hypothesis testing procedure, α refers to:

Options:
a) 1 – the level of significance
b) the critical value
c) the confidence level
d) level of significance

Answer: d
Explanation: α (alpha) is the probability of making a Type I error, i.e., rejecting the null hypothesis when it is actually true. It is also called the level of significance.

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9. If a hypothesis test leads to the rejection of the null hypothesis,

Options:
a) a Type II error must have been committed
b) a Type II error may have been committed
c) a Type I error must have been committed
d) a Type I error may have been committed

Answer: d
Explanation: If the null hypothesis is rejected, and if it was actually true, then a Type I error may have been committed. We don’t know for sure, hence “may have”.