Question

A researcher wants to estimate the difference in the means of two populations. A random sample of 36 items from the first population results in a sample mean of 430. A random sample of 49 items from the second population results in a sample mean of 460. The population standard deviations are 120 for the first population and 140 for the second population. From this information, a 95% confidence interval for the difference in population means is _______.

Select one:

a. -102.83 to 42.43

b. -27.6049 to 87.6049

c. -76.53 to 16.53

d. -95.90 to 35.90

Answer 1

SOLUTION:

From given data,

A researcher wants to estimate the difference in the means of two populations. A random sample of 36 items from the first population results in a sample mean of 430. A random sample of 49 items from the second population results in a sample mean of 460. The population standard deviations are 120 for the first population and 140 for the second population. From this information, a 95% confidence interval for the difference in population means is _______.

Where,

Population standard deviations are known so we calculate through normal distribution

= 430	= 460
= 120	= 140
= 36	= 49

95% confidence interval for the difference in population means is _______.

Confidence interval is 95%

95% = 95/100 = 0.95

= 1 - Confidence interval = 1-0.95 = 0.05

/2 = 0.05 / 2

= 0.025

Z_/2 = Z_0.025 = 1.96

(-) - Z_/2 * sqrt(/ + / ) <   - < (-) + Z_/2 * sqrt(/ + / )

(430-460) -1.96 * sqrt(120²/36 + 140²/49 ) <   - < (430-460) +1.96 * sqrt(120²/36 + 140²/49 )

-30 -1.96 * 28.284271247 <   - < -30+1.96 * 28.284271247

-30 - 55.43717164412 <   - < -30+55.43717164412

-85.4372 <   - < 25.4372

through normal distribution we got the answer as (-85.4372 to 25.4372) you didn't mention in your options please check it.

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