Page 405 - DMTH404_STATISTICS

Unit 29: Estimation of Parameters: Criteria for Estimates

29.7 Review Questions Notes

1. A random sample of 400 farms in certain year revealed that the average yield per acre of
sugarcane was 925 kgs with a standard deviation of 88 kgs.

(a) Determine the 95% confidence interval for the population mean.
(b) What should be the size of the sample if the width of 95% confidence interval
estimate of m is not more than 15?

Hint : (a) See example 5, (b) Î = 15/2.
2. A random sample of 100 sale receipts of a firm showed that its average sales per customer
are Rs 250 with a standard deviation of Rs 50 (assume that there is one receipt for each
customer).
(a) Determine the 99% confidence interval for the mean sales.
(b) How does the width of the confidence interval change if sample size is 400 instead?

(c) How many sale receipts should be included in the sample in order that a 98%
confidence interval has a maximum error of estimation equal to Rs 10.
Hint: (a) z = 2.58 and since s is not known, use S as its estimate. (b) Sample size is inversely
related to the width of Confidence interval. (c) z = 2.33.
3. A survey revealed that 30% of the persons of a state are suffering from a particular disease.
How many persons should be included in the sample so that the maximum width of the
95% confidence interval of proportion of persons suffering from the disease is 0.15 units?

2
z pq
Hint : n = 2 .
Î
4. A random sample of size 64 has been drawn from a population with standard deviation 20.
The mean of the sample is 80. (i) Calculate 95% confidence limits for the population mean.
(ii) How does the width of the confidence interval changes if the sample size is 256 instead?
Hint :  is given to be 20.
5. In a random sample of 100 articles taken from a large batch of articles, 10 are found to be
defective. Obtain a 95% confidence interval for the true proportion of defectives in the
batch.
Hint : See example 6.
6. A random sample of size 10 from a normal population gives the values 64, 72, 65, 70, 68, 71,
65, 62, 66, 67. If it is known that the standard error of the sample mean is 0.7 , find 95%
confidence limits for the population mean. Also find the population variance.

Hint : = 0.7.
n
Answers: Self Assessment

1. (i) T (ii) F (iii) F (iv) T (v) T (vi) T

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