Jessie filled a container of water with 200 milliliters. Zaria filled a different container with 400 milliliters. There are 1000
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Answer:
yes
Step-by-step explanation:
<u>Given: </u>
x_1= 180
n_1= 580
x_2= 238
n_2= 600
= 0.01
<u>Given claim: difference </u>
The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is equal to the value mentioned in the claim. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.
H_0:p_1=p_2
H_0:p_1p_2
<u>CRITICAL VALUE APPROACH </u>
The sample proportion is the number of successes divided by the sample size:
p_1=x_1/n_1=0.3103
p_2=x_2/n_2=0.40
p_p=(x_1+x_2)/(n_1+n_2) = 0.36
Determine the value of the test statistic:
z=(p_1-p_2) ÷ (√p_p(1-p_p)*√(1/n_1+1/n_2)
=-3.10
The critical values are the values corresponding to a probability of /2 = 0.025 and 1-
/2 = 0.975 in the normal probability table in the appendix:
z = ±2.575
The rejection region then contains all values below —2.575 and all values above 2.575.
If the value of the test statistic is within the rejection region, then the null hypothesis is rejected:
—3.10 < —2.575 ==> Reject H_0
There is sufficient evidence to support the claim that there is a difference in the proportion of individuals in these in favor of capital punishment for persons under the age of 18.
P-VALUE APPROACH
The sample proportion is the number of successes divided by the sample size:
p_1=x_1/n_1=0.3103
p_2=x_2/n_2=0.40
p_p=(x_1+x_2)/(n_1+n_2) = 0.36
Determine the value of the test statistic:
z=(p_1-p_2) ÷ (√p_p(1-p_p)*√(1/n_1+1/n_2)
=-3.10
The P-value is the probability of obtaining the value of the test statistic, or a value more extreme, assuming that the null hypothesis is true. Determine the P-value using table the normal probability table in the appendix:
P = P(Z < –3.10 or Z > 3.10) = 2P(Z < –3.10) = 2(0.0010) = 0.0020
If the P-value is smaller than the significance level, then reject the null hypothesis:
P < 0.01 ==> Reject H_0
There is sufficient evidence to support the claim that there is a difference in the proportion of individuals in these groups in for of capital punishment for persons under the age of 18.