# Statistical Methods-Standard Errors and Large Sample Tests (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 2 of 2

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## Question number: 1

» Statistical Methods » Standard Errors and Large Sample Tests

Appeared in Year: 2013

### Describe in Detail

The proportion of defective telephone instruments from the All-India basis was observed to be at 0.01. A new manufacturer of telephone instruments wants to estimate the proportion of defectives in his production lot. How many telephones should be sampled in order to estimate the fraction defective within 0.01 with 90 % confidence?

### Explanation

Let the proportion of defective telephone instruments from the All-India basis was observed to be at 0.01. The number of telephones should be sampled where the estimate fraction defective is p-p _{0} =0.01 and the true value of proportion of defective is 0.01. so, the test statistic for 90 % confidence is

Where ME = margin of error = 0.01

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## Question number: 2

» Statistical Methods » Standard Errors and Large Sample Tests

Appeared in Year: 2009

### Describe in Detail

A sample of 100 records on lengths of stay of patients in a hospital gave a standard deviation of days of stay as 4·9. In order to estimate the mean number of days of stay within 0·25 day with 95 % confidence, what should be the sample size?

### Explanation

Let the patients in a hospital gave a standard deviation of days of stay as 4.9. The mean number of days of stay within 0·25 day that is margin error is the estimate fraction days between the difference of estimated and the true number of days. So, the test statistic for 95 % confidence is

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