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Perform Hypothesis Testing
1.) We have given that,
"\\bar x = 40000"
"s= 1000"
"n = 50"
Degree of freedom = 50-1 = 49
"\\alpha = 0.05"
The following null and alternative hypothesis needed to be tested:
"H_0 : \\mu = 50000"
"H_1 : \\mu \\ne 50000"
We will use t test in this scenario.
Based on the information provided, the critical value for a two tailed test is "t_c = 2.009"
The t statistic is calculated as
"t = \\dfrac{\\bar x - \\mu}{\\dfrac{s}{\\sqrt n}}"
"= \\dfrac{40000-50000}{\\dfrac{1000}{\\sqrt 50}}"
"= -70.71"
Hence, "70.711 > 2.009 = t_c" it is concluded that null hypothesis is rejected.
Therefore, there is enough evidence to claim that the population mean is different than 50000, at 0.05 level of significance.
2.) Proportion of people who vote for him "= p = \\dfrac{925}{2500} = 0.37"
Hence, we can say that this significantly different from the percentage of potential voters of the candidate who requested the survey
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