I really need a help to answer this question with step by step! thank you!!! Sup
ID: 3132109 • Letter: I
Question
I really need a help to answer this question with step by step! thank you!!!
Suppose you ip a coin 100 times and get Heads on 62 of the ips. From this sample, it appears that the coin may be biased toward Heads. In this problem, you will evaluatewhether there is any evidence to support this claim.
a) If p = the proportion of Heads (out of all possible ips of this particular coin), compute ˆp and ˆq as determined by the sample described above.
b) To answer the question “Is this particular coin biased in favor of Heads?” what Null Hypothesis and Alternative Hypothesis should we use?
c) Before running the hypothesis test you set up in b), what Assumptions andConditions must be satised? Are they satised in this case?
d) Compute SD(ˆp), the Z-statistic, and the P-value for the hypothesis test you set up in part b).
e) What conclusion can you state for your hypothesis test?
g) Construct a 95% condence interval for p.
h) What is the margin of error for ˆp?
i) Suppose you ip the same coin 100 more times and use the same procedure tocalculate a 95% condence interval. True or false, and explain fully: you will arrive at thesame condence interval as before.
Explanation / Answer
a)
Here, x = 62, n = 100, so
p^ = x/n = 0.62 [ANSWER]
q^ = 1 - p^ = 0.38 [ANSWER]
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b)
Ho: p <= 0.50
Ha: p > 0.50 [ANSWER]
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c)
We assume that the trials are independent.
Also, as x = 62 > 5 and n - x = 38 > 5, then the conditions are satisfied.
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d)
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 = 0.62
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.05 [ANSWER, STANDARD ERROR]
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Getting the z statistic,
z = (p^ - po)/sp = 2.4 [ANSWER, Z STATISTIC]
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As this is a 1 tailed test, then, getting the p value,
p = 0.008197536 [ANSWER, P VALUE]
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e)
As P < 0.05, we REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence that the coin is biased toward heads.
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