UNIT 5 QUESTION BANK
PART A
5 A Define null hypothesis
5 A Define Alternative Hypothesis
5 A What is the Z-test used for in hypothesis testing?
5 A What is the main difference between Z-test and t-test?
5 A Mention one condition for applying the t-test
5 A What is the purpose of the ANOVA test?
5 A Define Population and Sample
5 A How does the p-value help in hypothesis testing?
5 A How does the F-test help compare variances?
5 A Identify the purpose of a chi-square test and its use in research.
5 A Why is the F-test important in comparing variances?
How can you interpret the result of a Z-test statistic?
5A
PART B
5 B Explain the procedure of conducting a one-sample Z-test.
5 B Differentiate between the Z-test and the Student's t-test in terms of sample size and application
5 B Discuss the properties and uses of the chi-square distribution.
5 B Outline the procedure for conducting a chi-square goodness-of-fit test.
5 B How do you interpret the results of a one-way ANOVA test?
5 B Explain the concept of degrees of freedom in the context of chi-square and t-tests.
5 B A factory claims that its bulbs last on average 500 hours. A random sample of 100 bulbs showed that
the mean life was 495 hours with a standard deviation of 15 hours. Test at the 5% significance level if
the factory’s claim is correct.
5 B A sample of 30 students has a mean score of 78 in a test. The population mean score is 75 with a
standard deviation of 10. Test at the 1% significance level whether the sample mean is significantly
different from the population mean.
5 B A bag contains 500 candies of six different colors. The following observed frequencies are noted: Red:
85, Green: 95, Blue: 90, Yellow: 80, Orange: 70, Purple: 80. Test if the candies are equally distributed
among the colors at the 5% significance level.
5 B A biologist is studying the number of bird sightings in a particular forest over the course of one week.
The following table shows the number of sightings for each day of the week
Day Sun Mon Tue Wed Thu Fri Sat Total
No. of
13 15 9 11 12 10 14 84
Sightings
Test whether the bird sightings are uniformly distributed over the week using the chi-square goodness
of fit test at the 5% significance level.
PART C
5 C Explain in detail the procedure for conducting a large sample test using the Z-test. Include an example
5 C Explain the difference between one-tailed and two-tailed tests.
5 C Illustrate Standard Error in Statistics
5 C Explain the difference between one-tailed and two-tailed tests.
5 C Explain (i) population, (ii) Sample (iii) Parameter (iv) Statistic
5 C Two samples of sizes 20 and 25 have the following variances:
Sample 1: Variance = 25, Sample 2: Variance = 36.
Test at the 5% significance level whether the variances are equal.
5 C A researcher wants to test if the average scores of three different teaching methods are the same. The
scores are as follows:
Method 1: 85, 87, 88, 90, 91
Method 2: 80, 82, 83, 86, 88
Method 3: 78, 80, 82, 85, 86
Test at the 5% significance level.
5 C A company claims that their average product lifespan is 500 hours. A sample of 200 products is tested,
and the sample mean is found to be 495 hours, with a standard deviation of 10 hours. Test at the 5%
significance level whether the claim is true.
5 C A study is conducted to see if there is an association between smoking and gender. The observed data
is as follows:
Non-
Gender Smoker Total
Smoker
Male 40 60 100
Female 20 80 100
Total 60 140 200
Test if smoking is independent of gender at the 5% significance level.
5 C A biologist is studying the effect of two different fertilizers on the growth of plants. After one month, the
average growth of 50 plants treated with Fertilizer A is 15 cm, and the average growth of 50 plants
treated with Fertilizer B is 18 cm. The standard deviation of the growth for Fertilizer A is 4 cm, and for
Fertilizer B, it is 5 cm. Test at the 5% significance level if the average growth of plants differs
significantly between the two fertilizers.
PART D
5 D A company wants to test whether different departments (A, B, and C) have different levels of
productivity. The productivity scores are as follows:
Department A: 15, 16, 18, 20, 21
Department B: 17, 19, 20, 22, 23
Department C: 14, 15, 17, 19, 20
Perform a one-way ANOVA to test at the 1% significance level.
5 D A researcher is comparing the average growth rates of two plant species, A and B, after being exposed
to a particular nutrient. The data is as follows:
• Species A: Sample size = 50, Sample mean = 20 cm, Standard deviation = 4 cm.
• Species B: Sample size =
• 50, Sample mean = 22 cm, Standard deviation = 5 cm.
Test at the 5% significance level if there is a significant difference in the average growth between the
two species.
5 D A company is testing two different types of pesticides to determine which is more effective in reducing
pest population. After conducting trials, the following results were obtained:
• Pesticide A: Sample size = 20, Sample mean = 50, Standard deviation = 7.
• Pesticide B: Sample size = 25, Sample mean = 47, Standard deviation = 6.
Test at the 5% significance level if there is a significant difference in the effectiveness of the two
pesticides using a T-test.
