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3 years ago

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Small sample: During an economic downturn, companies were sampled and asked whether they were planning to increase their workfor

ce. Only of the companies were planning to increase their workforce. Use the small-sample method to construct a confidence interval for the proportion of companies that are planning to increase their workforce. Round the answers to at least three decimal places. A confidence interval for the proportion of companies that are planning to increase their workforce is .

1 answer:

leva [86]3 years ago

7 0

Complete Question

The complete question is shown on the first uploaded image

Answer:

The confidence level interval is $0.016 \le C \le 0.404$

Step-by-step explanation:

The sample size is $n = 20$

The number planning to increase workforce is $x = 3$

The confidence level is $c = 98$ %

The value of proportion for a plus 4 method is

$p = \frac{x+2}{n+4}$

substituting values

$p = \frac{3+2}{20+4}$

$p =0.21$

The z-critical value at confidence level of 98% is

$z_{c}=z_{0.98} = 2.33$

This values is obtained from the standard normal table

The confidence level interval can be mathematically represented as

$C =p \ \pm z_{c} * \sqrt{\frac{p(1-p)}{n+4} }$

substituting values

$C = 0.21 \pm 2.33 * \sqrt{\frac{0.21(1- 0.21)}{20 +4} }$

$C = 0.21 \pm 0.194$

=> $0.016 \le C \le 0.404$

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