is néédéd to cut margil e Tim you c. (1 points)What sample size interval to 1.5%
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Question
is néédéd to cut margil e Tim you c. (1 points)What sample size interval to 1.5%? Use 51% as your best guess for #2.( 5points)In a study conducted recently 567 out of 1072 people surveyed expressed preference for chocolate ice cream over othe r flavors. et p be the proportion of the population surveyed that prefers chocolate ice cream. At 5% significance level do the data presents evidence at majority (over half) of people from surveyed population prefer chocolate ice cream? Test appropriate hypothesis. Use following steps: a) state both hypotheses: Ho b) compute the test statistics. Ha : c) compute a p-value d) decide if you reject null hypothesis or not, Circle one: e) Answer question posed in the problem, use a complete sentence. Reject Ho Do not reject HoExplanation / Answer
Part a
The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: The population proportion of the people who prefer chocolate ice cream is 50%.
Alternative hypothesis: Ha: The population proportion of the people who prefer chocolate ice cream is more than 50%.
In symbolic notation,
Null hypothesis: H0: p = 0.5
Alternative hypothesis: Ha: p > 0.5
Part b
Test statistic formula is given as below:
Z = (P – p) / sqrt(pq/n)
Where, q = 1 – p
We are given
Number of items of interest = X = 567
Sample size = n = 1072
Sample proportion = P = X/n = 567/1072 = 0.52891791
Population proportion = p =0.5, so q = 1 – p = 1 – 0.5 = 0.5
Z = (0.52891791 – 0.5)/sqrt(0.5*0.5/1072)
Z = (0.52891791 – 0.5)/ 0.0153
Z = 1.8936
Part c
P-value = 0.0291
(by using z-table for = 0.05)
Part d
P-value < = 0.05,
So, we reject the null hypothesis H0
Part e
At 5% level of significance, there is sufficient evidence to conclude that majority of people from surveyed population prefer chocolate ice cream.
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