In a poll of 500 adults in July 2010, 270 of those polled said that schools shou
ID: 3440036 • Letter: I
Question
In a poll of 500 adults in July 2010, 270 of those polled said that schools should ban sugary snacks and soft drinks. Complete parts a and b below. a. Do a majority of adults (more than 50% support a ban on sugary snacks and soft drinks? Perform a hypothesis test using a significance level of 0.05 State the null and alternative hypotheses. Note that p is defined as the population proportion of people who believe that schools should ban sugary foods. OA Ho: p 0.50 Ha p 4 0.50 OB. Ho: p 0.54 Ha p> 0.54 OC. Ho: p 0.50 OD. Ho: p 0.50 Ha p 0.50 Find the value of the test statistic z. z Round to two decimal places as needed.) Find the value of the corresponding p-value for this test statistic z p-value Round to three decimal places as needed.) Do you reject or not reject the null hypothesis? n Reiert HExplanation / Answer
a)
A majority is p > 0.50, which is the claim and the alternative hypothesis. Hence,as the null hypothesis is the opposite of the null,
Ho: p < 0.50
Ha: p > 0.50 [ANSWER]
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b)
Formulating the null and alternatuve hypotheses,
Ho: p <= 0.5
Ha: p > 0.5
As we see, the hypothesized po = 0.5
Getting the point estimate of p, p^,
p^ = x / n = 0.54
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.02236068
Getting the z statistic,
z = (p^ - po)/sp = 1.788854382 [ANSWER, TEST STATISTIC Z]
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As this is a 1 tailed test, then, getting the p value,
p = 0.036819135 [answer, p value]
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As, significance level = 0.05
Comparing p < significance value, we REJECT THE NULL HYPOTHESIS. [reject Ho]
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