Worksheet: Confidence Intervals for Population Means

In this worksheet, we will practice calculating 90%, 95%, and 99% confidence intervals for the population means.

Q1:

The weights of packets of chips are known to be distributed with a variance of 2.56 grams. A sample of 100 packs were tested and the mean weight was 24.1 grams.

Calculate a 9 9 % confidence interval for the population mean 𝜇 .

  • A 2 3 . 8 3 𝜇 2 4 . 3 6
  • B 2 3 . 7 8 𝜇 2 4 . 4 1
  • C 2 3 . 7 8 𝜇 2 4 . 5 1
  • D 2 3 . 6 9 𝜇 2 4 . 5 1
  • E 2 3 . 8 3 𝜇 2 4 . 5 1

Q2:

A sample of the heights of 𝑛 people from a population resulted in a sample mean of 𝑥 meters. Given that the standard deviation, 𝜎 , is known, which of the following represents a 9 0 % confidence interval for the population mean?

  • A 𝑥 1 . 9 6 𝜎 𝑛 , 𝑥 + 1 . 9 6 𝜎 𝑛
  • B 𝑥 1 . 6 4 5 𝜎 𝑛 1 , 𝑥 + 1 . 6 4 5 𝜎 𝑛 1
  • C 𝑥 1 . 9 6 𝜎 𝑛 1 , 𝑥 + 1 . 9 6 𝜎 𝑛 1
  • D 𝑥 1 . 6 4 5 𝜎 𝑛 , 𝑥 + 1 . 6 4 5 𝜎 𝑛
  • E 𝜇 1 . 6 4 5 𝜎 𝑛 , 𝜇 + 1 . 6 4 5 𝜎 𝑛

Q3:

The number of hours students spend on homework each week is known to be distributed with a standard deviation of 3.21 hours. A sample of 50 students were asked how many hours they spend doing homework in a week and the results are given in the table.

Hours 3 4 5 6 7 8 9 10 11
Number of Students 4 5 8 10 4 7 9 2 1

Find the sample mean.

Calculate a 9 5 % confidence interval for the population mean.

  • A ( 5 . 6 7 , 7 . 4 5 )
  • B ( 5 . 9 1 , 7 . 2 1 )
  • C ( 5 . 4 , 7 . 7 3 )
  • D ( 5 . 8 1 , 7 . 3 )
  • E ( 5 . 6 7 , 7 . 3 )

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