Question

1. A prison official wants to estimate the proportion of cases
of recidivism. Examining the records of **217**
convicts, the official determines that there are
**80** cases of recidivism. Find the margin of error
for a **95**% confidence interval estimate for the
population proportion of cases of recidivism. (Use
3 decimal places.)

2. A prison official wants to estimate the proportion of cases
of recidivism. Examining the records of **204**
convicts, the official determines that there are
**32** cases of recidivism. Find a point estimate of
the population proportion of cases of recidivism. (Round
your answer to three decimal places.)

3. A prison official wants to estimate the proportion of cases
of recidivism. Examining the records of **298**
convicts, the official determines that there are
**93** cases of recidivism. Find the standard error
for the population proportion of cases of
recidivism. (Round to 3 decimal places.)

4. A prison official wants to estimate the proportion of cases
of recidivism. Examining the records of **241**
convicts, the official determines that there are
**63** cases of recidivism. Find the lower limit of
the **90**% confidence interval estimate for the
population proportion of cases of recidivism. (Round to 3 decimal
places.)

5. A quality control engineer is interested in estimating the
proportion of defective items coming off a production line. In a
sample of **336** items, **48** are
defective. Calculate a **upper** confidence limit for
a **95.0**% confidence interval for the proportion of
defectives from this production line. (Use 3 decimal
places in calculations and in reporting your answer.)

Answer #1

**Answer:**

**1.**

Given,

p^ = x/n = 80/217 = 0.369

Here at 95% CI, z value is 1.96

Margin of error = z*sqrt(p^(1-p^/n)

substitute values

= 1.96*sqrt(0.369(1-0.369)/217)

E = 0.064

**2.**

Point estimate p^ = x/n

= 32/204

= 0.157

**3.**

p^ = 93/298 = 0.312

SE = sqrt(p^(1-p^)/n)

substitute values

= sqrt(0.312(1-0.312)/298)

= 0.027

**4.**

p^ = 63/241 = 0.2614

Here at 90% CI, z value is 1.645

Lower limit = p^ - z*sqrt(p^(1-p^)/n)

substitute values

= 0.2614 - 1.645*sqrt(0.2614(1-0.2614)/241)

= 0.2614 - 0.0466

= 0.215

**5.**

p^ = 48/336 = 0.1429

Here at 95% CI, z value is 1.96

Upper limit = p^ + z*sqrt(p^(1-p^)/n)

substitute values

= 0.1429 + 1.96*sqrt(0.1429(1-0.1429)/336)

= 0.1803

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