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.

Answer:

a)H0: µ1= µ2

Ha: µ1≠µ2

n₁=10

x₁=18

s₁²=25

n₂=8

x₂=12

s₂²=16

Pooled Variance = (10*25+8*16)/(10+8) =21

Pooled standard deviation=√21 =4.5825757

Standard error=4.5825757*√(1/10+1/8)

=2.17371

t-statistic= difference of means/standard error

=(18-12)/2.17371

=2.760258

Degree of freedom= 10+8-2 = 16

t-critical= 2.12

As t-calculated is greater than t-critical value, we have enough evidence to reject the null hypothesis and thus we conclude that µ1≠µ2.

b)H₀: Electrification and under cage has same impact on tillers

H_a: Electrification has greater impact on tillers

As the p-value is less than the level of significance we have enough evidence to reject the null hypothesis and thus we conclude that Electrification has real impact on tillers.

c) H0: there is no difference between males' and females' voting preferences

Ha: there is significant difference between males'and females'voting preferences.

Expected value = Row total*Column total/Grand total

Chi-square = sum{(O-E)²/E}

=10.6666667

P-VALUE is calculated in excel sheet using the formula=chi.dist(10.666667,5) =0.058404547

As the p-value is greater than the level of significance (0.05), we don't have enough evidence to reject the null hypothesis and thus we conclude that the men's voting preferences doesn't differ significantly from the  women's preferences.

please use this google drive link to download the answer file.

https://drive.google.com/file/d/1N6YvmZ5auu_6OFnVtkR_j-cE2GZYpnmB/view?usp=sharing

note: if you have any trouble in viewing/downloading the answer from the given link, please use this below guide to understand the whole process.

https://helpinhomework.org/blog/how-to-obtain-answer-through-google-drive-link