Question

1. In a recent survey of 910 randomly selected likely voters in Indiana, 477 said they oppose a proposal to tax internet sales. Based on this sample, can we say at the 5% alpha level that at least 50% of the voters in Indiana oppose the tax? Answer this question by using the normal approximation to the binomial to conduct the appropriate 1-sided test (that is, write the hypotheses and find the test statistic) by hand. (Remember, by-hand work does not need to be put in your paper.) Then confirm your results using Minitab. Remember, when asked to confirm results or create something with Minitab, the Minitab output must be copied and pasted into your .

Answer 1

given data are:-

n = 910

level of significance ()= 0.05

checking normal approximation to binomial:-

so, we can use the normal approximation to the binomial to conduct the test.

hypothesis:-

test statistic:-

using minitab to solve this:-

steps:-

stat basic statistics 1 proportion select summarized data in number of events type 477,in number of trials type 910 tick perform hypothesis test in hypothesized proportion type 0.50 options in confidence level type 95.0 , in alternative hypothesis select proportion hypothesized proportion ,in method select normal approximation ok ok.

your output be:-

Test and CI for One Proportion

Method

p: event proportion

Normal approximation method is used for this analysis.

Descriptive Statistics

N	Event	Sample p	95% Upper Bound for p
910	477	0.524176	0.551407

Test

Null hypothesis	H₀: p = 0.5
Alternative hypothesis	H₁: p < 0.5

Z-Value	P-Value
1.46	0.928

decision:-

p value = 0.928 >0.05

so, we fail to reject the null hypothesis.

conclusion:-

there is sufficient evidence to say at the 5% alpha level that at least 50% of the voters in Indiana oppose the tax

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