Answer:
The null and alternative hypothesis for this question is H₀: p = 0.50 and H₁: p ≠ 0.50 respectively.
Hence, option B is correct.
Upper H0: pequals=0.5, Upper H1: pnot equals≠0.5
The hypothesis test shows that there is enough evidence to conclude that the proportion of the population that favour the use of federal tax dollars to fund medical research using stem cells obtained from human embryos is not 0.50 like that of a coin toss. That is, the politicians claim is false.
Step-by-step explanation:
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually contains the signs ≠, < and > depending on the directions of the test.
For this question, the politician claims that people don't really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. A coin toss has a 50-50 probability, with a proportion 0.5 for heads and another 0.5 for tails.
Hence, the null hypothesis for this question would be that there is evidence to suggest that the proportion of the population that favour the use of federal tax dollars to fund medical research using stem cells obtained from human embryos is 0.50 like that of a coin toss. That is, the politicians claim is true.
And the alternative hypothesis is that there is significant evidence to conclude that the proportion of the population that favour the use of federal tax dollars to fund medical research using stem cells obtained from human embryos is not 0.50 like that of a coin toss. That is, the politicians claim is false.
Mathematically, if p is the population proportion that favour the use of federal tax dollars to fund medical research using stem cells obtained from human embryos.
The null hypothesis is represented as
H₀: p = 0.50
The alternative hypothesis is represented as
H₁: p ≠ 0.50
To do this test, we will use the z-distribution because although, no information on the population standard deviation is known, the sample size is large enough for a z-test statistic to work.
So, we compute the test statistic
z = (x - μ)/σₓ
x = sample proportion = (485)/(485+396) = 0.55 (excluding the ones that were unsure)
μ = p₀ = The proportion we are comparing against = 0.50
σₓ = standard error = √[p(1-p)/n]
where n = Sample size = 485 + 396 = 881
σₓ = √[0.55×0.45/881] = 0.0167609874 = 0.01676
z = (0.55 - 0.50) ÷ 0.01676
z = 2.98 = 2.98
checking the tables for the p-value of this z-statistic
Degree of freedom = df = n - 1 = 881 - 1 = 880
Significance level = 0.10
The hypothesis test uses a two-tailed condition because we're testing in both directions (greater than or less than).
p-value (for z = 2.98, at 0.10 significance level, df = 880, with a two tailed condition) = 0.002882
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.10
p-value = 0.002882
0.002882 < 0.10
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the proportion of the population that favour the use of federal tax dollars to fund medical research using stem cells obtained from human embryos is not 0.50 like that of a coin toss. That is, the politicians claim is false.
Hope this Helps!!!
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