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 99% confidence interval for the population mean 𝜇.

  • A23.83𝜇24.36
  • B23.69𝜇24.51
  • C23.78𝜇24.51
  • D23.83𝜇24.51
  • E23.78𝜇24.41

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 90% confidence interval for the population mean?

  • A𝑥1.645𝜎𝑛,𝑥+1.645𝜎𝑛
  • B𝜇1.645𝜎𝑛,𝜇+1.645𝜎𝑛
  • C𝑥1.645𝜎𝑛1,𝑥+1.645𝜎𝑛1
  • D𝑥1.96𝜎𝑛1,𝑥+1.96𝜎𝑛1
  • E𝑥1.96𝜎𝑛,𝑥+1.96𝜎𝑛

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.

Hours34567891011
Number of Students4581047921

Find the sample mean.

Calculate a 95% confidence interval for the population mean.

  • A(5.4,7.73)
  • B(5.81,7.3)
  • C(5.67,7.45)
  • D(5.91,7.21)
  • E(5.67,7.3)

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