a) Two sample of size 10 and 8 had sample mean 18cm and 12cm with variances 25 and 16

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a) Two sample of size 10 and 8 had sample mean 18cm and 12cm with variances 25 and 16. Supposing that the samples have been drawn from normal populations. Test H₀: µ₁= µ₂ at 5% level of significance.

b)     Eights pots, growing three barley plants each, were exposed to high tension discharge while nine similar pots were enclosed in an earthed wire cage. The number of tillers (shoots) in each pot was as follows:

Caged: 17, 27, 18, 25, 27, 29, 27, 23, 17.

Electrified: 16, 16, 20, 16, 21, 17, 15, 20.

Discuss whether electrification exercises any real effect on tillers.

c) A Public Opinion poll surveyed a simple random sample of 800 voters. Respondents were classified by gender (male or female) and by voting preference (PPP, PLMN, or Independent). Results are shown in the contingency table.

Gender

                                 Voting Preferences

PPP

PLMN

Independent

Male

100

150

50

Female

150

300

50

 

Required: Is there a gender gap? Do the men's voting preferences differ significantly from the  women's preferences? State the Hypothesis. Use a 0.05 level of significance.