Significance Test for Means

The weight of the average 6th grade student's backpack (with books in it) is 18.4 lbs. The principal of the school thinks that the backpack does not weight 18.4 lbs. What is the null and alternate hypothesis?

• H₀ = 18.4
  H_a = 18.4

• H₀ = 18.4
  H_a > 18.4

• H₀ = 18.4
  H_a < 18.4

• H₀ = 18.4
  H_a ≠ 18.4

Which test do we run for means?

• Z-Test

• T-Test

• 1-PropZTest

• 1-MeanTTest

A manufacturer claims that his tires last at least 40,000

miles. A test on 25 tires reveals that the mean life of a tire

is 39,750 miles, with a standard deviation of 387 miles.

Test the Manufacturer’s claim at α = .01.

• Reject Ho

• Reject Ha

• Fail to reject Ho

• Fail to reject Ha

H₀: μ = k

H₁: μ ≠ k

• Left-tailed test

• Two-tailed test

• Right-tailed test

• A) Ho: The mean number of days 9th grade students absent is equal to the mean number of days 12th grade students are absent.
  Ha: The mean number of days 9th grade students absent is less than the mean number of days 12th grade students are absent.
• B) Ho: The mean number of days 12th grade students absent is less than the mean number of days 9th grade students are absent.
  Ha: The mean number of days 12th grade students absent is equal to the mean number of days 9th grade students are absent.
• C) Ho: The mean number of days 12th grade students absent is equal to the mean number of days 9th grade students are absent.
  Ha: The mean number of days 9th grade students absent is greater than the mean number of days 12th grade students are absent. 
• D) Ho: The mean number of days 12th grade students absent is equal to the mean number of days 9th grade students are absent.
  Ha: The mean number of days 12th grade students absent is less than the mean number of days 9th grade students are absent.

The U.S. Census Bureau reported that the mean area of U.S. homes built in 2009 was 2,438 square feet.  Assume that a simple random sample of 20 homes built in 2010 had a mean area of 2,514 square feet, with a standard deviation of 225 square feet.  Can you conclude that the mean area of homes built in 2010 is greater than that of homes built in 2009?  Use 0.01 level of significance.

The p-value is ​ (a)   > ​ (b)   ; thus, ​ (c)   the null hypothesis.

​ (d)   evidence to conclude that the mean area of homes built in 2010 is greater than that of homes built in 2009.

• 0.0737

• 0.0654

• we fail to reject

• we reject

• There is not enough

• There is enough

• 0.01

• 0.05

To test a claim about a mean, when the population standard deviation is unknown we use:

• z procedures

• Pythagorean Theorem

• t procedures

• np > 10 and n(1-p) > 10

A random sample of 100 pairs of ladies’ shoes had a mean size of 8.3. Assume the population standard deviation is 1.5.  Can you conclude that the mean size of ladies’ shoes differs from 8?  Use the 0.01 level of significance.

• 8.3

• x̄

• 8

• n

• 100

• s

• N/A

• µ

• 1.5

• σ

A random sample of 49 medical doctors in LA showed that they worked an average of 53.1 hours/week with a standard deviation of 7.2 hours/week. If the California average is 60 hours/week, does this give evidence that the LA doctors work significantly less than the rest of California?

• One-Sample T Test for a Mean

• One-Sample Z Test for a Mean

• One-Sample T Test for a Proportion 

• One-Sample Z Test for a Proportion

A random sample of 100 pairs of ladies’ shoes had a mean size of 8.3. Assume the population standard deviation is 1.5.  Can you conclude that the mean size of ladies’ shoes differs from 8?  Use the 0.01 level of significance.

p-value is ​ (a)   ​ (b)   0.01 hence ​ (c)   the null hypothesis.

​ (d)   evidence to conclude that the mean size of ladies' shoes differs from 8.

• There is not enough

• 0.0482

• >

• we fail to reject

• We reject

• <

• There is enough

• 0.485