The principal at a local high school claims that the proportion of high school males taking AP statistics is the same as the proportion of high school females taking statistics. Upon surveying 30 males and 28 females. The principal found that 6 males and 7 females are taking AP statistics. Although the proportions of these two populations are close, can the principal state that they are, in fact, statistically the same?
A Two-Sample Hypothesis Test
The principal at a local high school claims that the proportion of high school males taking AP statistics is the same as the proportion of high school females taking statistics. Upon surveying 30 males and 28 females. The principal found that 6 males and 7 females are taking AP statistics. Although the proportions of these two populations are close, can the principal state that they are, in fact, statistically the same? (Assume a 5% level of significance.)
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1. Which of the following null and alternative hypotheses match this scenario?
A---H0:Δμ=0H0:Δμ=0
Ha:Δμ≠0Ha:Δμ≠0
B---H0:Δp=0H0:Δp=0
Ha:Δp>0Ha:Δp>0
C---H0:Δp=0H0:Δp=0
Ha:Δp≠0Ha:Δp≠0
2. Which type of test should be applied?
A---The alternative hypothesis indicates a right-tailed test.
B---The alternative hypothesis indicates a left-tailed test.
C---The alternative hypothesis indicates a two-tailed test.
3. Which type of distribution should be applied?
A---The required distribution is a Normal Distribution.
B---The required distribution is Student's t-Distribution.
C---The required distribution is a Binomial Distribution approximated by a Normal Distribution.
4. Calculate the p-value from this hypothesis test.
p= (Include four decimal places.)
5. Which of the following is an appropriate conclusion?
A---Given that p<αp<α at a 5% level of significance, from the sample data, there is sufficient evidence to conclude that the means are statistically the same.
B---Given that p>αp>α at a 5% level of significance, from the sample data, there is sufficient evidence to conclude that the means are statistically the same.
C---Given that p>αp>α at a 5% level of significance, from the sample data, there is not sufficient evidence to conclude that the means are statistically the same.
D---Given that p<αp<α at a 5% level of significance, from the sample data, there is sufficient evidence to conclude that the difference in means is statistically significant.
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