Testing a Hypothesis in Statistics

The quality assurance officer of a manufacturer claims that the lifetime of a certain electrical part is normally distributed with mean 100 hours and standard deviation 20 hours. To verify this claim, a random sample of 30 bulbs was tested and the average lifetime of the parts in this sample is 98 hours. Why is performing a hypothesis test necessary?

• The lifetime of the electrical part is normally distributed.

• Hypothesis tests are necessary in all claims which involve electrical parts.

• The average lifetime calculated from the random sample is being used to make conclusions on the population mean.

• The average lifetime calculated from the sample is less than the mean of 100 hours in the claim.

Past experience indicates that the time required for high school students to complete a standardized test is normally distributed. A random sample of 300 high school students consisting of 150 male students and 150 female students took the test. We wish to test the hypothesis that the average time for female students to complete the test is higher than male students. Assume population variances are equal. Which of the following test should be used?

• One-sample t-test

• Two-sample pooled t-test

• Two-sample non-pooled t-test

• Two dependent sample t-test

Answer explanation

Since the population standard deviations are unknown but assumed to be equal, we use the pooled t-test.

An online learning platform offers an introductory statistics course. Two years ago, it was found that the mean number of hours that the course participants spend on the online course materials is 2.1 hours per week. Recently, the platform provided conducted a survey on a sample of 40 randomly selected course participants to find out the amount of time they spent on the online course materials in a week. From the sample, the mean number of hours spent is 2.3 hours with a standard deviation of 0.7 hours. A hypothesis test is performed to determine if the data provide sufficient evidence to conclude that, on average, the recent batch of course participants spent more time than those two years ago on the online course materials. Calculate the test statistic.

Mathematical Equivalence

ON

A study conducted a few months ago indicated that 28% of working adults in Klang Valley has proper sitting posture when working at the office desk. Since then, a campaign is launched to create awareness on proper sitting posture and results of a new study show that out of the 200 randomly sampled working adults 68 are aware of proper sitting posture when working at the office desk. A hypothesis test is performed to determine if there is significant evidence to suggest that the proportion of working adults in Klang Valley who are aware of proper sitting posture when working has increased after the implementation of the campaign. Calculate the test statistic.

Past experience indicates that the time required for high school students to complete a standardized test is normally distributed. A random sample of 102 high school students consisting of 52 male students and 50 female students took the test. We wish to test the hypothesis that the average time for female students to complete the test is higher than male students. Assume population variances are equal. What is the critical value?

• 1.645

• 1.660

• 1.96

• 1.984

Caroline thinks she can flip a coin so it lands showing heads more often with her right hand. She flipped a coin 40 times with each hand. She wants to test whether she gets more heads with her right hand than her left hand. (Assume all conditions have been met.)

H₀: p_R - p_L = 0

H₁: p_R - p_L > 0

Which of the following would be an appropriate test statistic for Caroline's test?

• 
• 
• 
• 
• 

This is a ________ test.

• two-tailed

• left-tailed

• right-tailed

• equal-tailed

• two-tailed

• left-tailed

• right-tailed

• equal-tailed

Which one of the following is calculated from the sample data and used as a basis for deciding whether the null hypothesis should be rejected?

• p-value

• Sample statistic

• Test statistic

• Critical value

Answer explanation

The test statistic is calculated from sample data, using values such as the sample mean, sample size and/or sample standard deviation. Therefore, test statistic is expected to be different from sample to sample.

Past experience indicates that the time required for high school students to complete a standardized test is a normal random variable with a mean of 35 minutes. A random sample of 20 high school students took an average of 33.1 minutes to complete this test with a standard deviation of 4.3 minutes. If we wish to test the hypothesis that population mean is 35 minutes against the alternative that population mean is less than 35 minutes, we use the one-mean z-test.

• True

• False

Answer explanation

We use the t-test since population standard deviation is unknown. The standard deviation given in the question is calculated from the sample.