Critical Values: z0.005 = 2.575, z0.01 = 2.325, z0.025 = 1.96, z0.0

Maggenifh

Maggenifh

Answered question

2021-12-04

Critical Values: z0.005=2.575,z0.01=2.325,z0.025=1.96,z0.05=1.645,z0.1=1.282 
When d.f.=31:t0.005=2.744,t0.01=2.453,t0.025=2.040,t0.05=1.696t0.1=1.309 
774 men from the New Model Army, 226 from the New Model Army, and 226 from the Royalist Army were included in a random sample of the 774 soldiers who took part in the Battle of Preston. Use a 0.05 significance level to test the claim that fewer than one quarter of the soldiers were Royalist

Answer & Explanation

Feas1981

Feas1981

Beginner2021-12-05Added 16 answers

Step 1
It is given that,
X226
n774
Sample proportion, p^xn=2267740.292
A researcher claims that fewer than one quarter of the soldiers were Royalist.
Thus, the null and alternative hypothesis are:
H0:p0.25
H1:p<0.25
Step 2
The standardized test statistic can be calculated as:
Z=p^pp(1p)n=0.2920.250.25(10.25)1200=2.698
The level of significance, =0.05
Form the Z table, the critical value at the level of significance (0.05)is=1.645.
Conclusion:
Since.
Calculated Statistic Z=2.698>|Critical value|=|1.645|, We reject the Null hypothesis.
Therefore, it is concluded that fewer than one quarter of the soldiers were Royalist.

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