Total Frequency = 14 + 18 + 13 + 34 = 79
As each of the above event should be equally likely, therefore the expected frequency for each of the outcomes mentioned should be (79/4) = 19.75
Therefore the chi square test statistic here is computed as:
Therefore 14.4177 is the test statistic value here.
Suppose you want to test how fair is the coin. You conduct the following experiment. You...
Question 2 Suppose you have a fair coin (a coin is considered fair if there is an equal probability of being heads or tails after a flip). In other words, each coin flip i follows an independent Bernoulli distribution X Ber(1/2). Define the random variable X, as: i if coin flip i results in heads 10 if coin flip i results in tails a. Suppose you flip the coin n = 10 times. Define the number of heads you observe...
3. (25 pts) A Truly FAIR COIN: Because actual coins are not truly balanced, P - the ACTUAL probability of HEAD for our old, battered coin - may differ substantially from 1/2. The famous Mathematician John Von-Neumann came up with the following proposal for using our possibly unfair coin to simulate a truly fair coin that always has PROB(HEAD)=PROB(TAIL) = 1/2, as follows: • (i) toss the UNFAIR coin twice. This is the experiment E. • (ii) IF you got...
Suppose we suspect a coin is not fair we suspect that it has larger chance of getting tails than heads, so we want to conduct a hypothesis testing to investigate this question. a:(4 pts) Let p be the chance of getting heads, write down the alternative hypothesis Ha and the null hypothesis Ho in terms of p. b: (5 pts) In order to investigate this question, we flip the coin 100 times and record the observation. Suppose we use T...
Q2 (15) Suppose we suspect a coin is not fair – we suspect that it has larger chance of getting tails than heads, so we want to conduct a hypothesis testing to investigate this question. a:(4 pts) Let p be the chance of getting heads, write down the alternative hypothesis H, and the null hypothesis Ho in terms of p. b: (5 pts) In order to investigate this question, we flip the coin 100 times and record the observation. Suppose...
2. Suppose we want to test whether a coin is fair (that is, the probability of heads is p = .5). We toss the coin 1000 times, and record the number of heads. Let T denote the number of heads divided by 1000. Consider a test that rejects the null hypothesis that p=.5 if T > c. (a) Write down a formula for P(T>c) assuming p = 0.5. (This formula may be compli- cated, but try to give an explicit...
Perform the following experiment: Flip a coin 30 times. a) Using Maximum Likelihood Estimation, develop a point estimate of the probability that the coin will land on tails. b) Develop 95% and 99% confidence intervals for the probability the coin will land on tails. c) Test the null hypothesis that the coin is "fair."
You suspect that a coin is biased such that the probability heads is flipped (instead of tails) is 52%. You flip the coin 51 times and observe that 31 of the coin flips are heads. The random variable you are investigating is defined as X = 1 for heads and X = 0 for tails, and you wish to perform a "Z-score" test to test the null hypothesis that H0: u = 0.52 vs. the alternative hypothesis Ha: u > 0.52....
In order to test whether a certain coin is fair, it is tossed ten times and the number of heads (X) is counted. Let p be the "head probability". We wish to test the null hypothesis: p = 0.5 against the alternative hypothesis: p > 0.5 at a significance level of 5%. (a) Suppose we will reject the null hypothesis when X is smaller than h. Find the value of h. (b) What is the probability of committing a type...
Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How many times would we have to flip the coin in order to obtain a 98% confidence interval of width of at most .19 for the probability of flipping a head? a) 150 b) 149 c) 117 d) 116 e) 152
For this question, you will flip fair coin to take some samples and analyze them. First, take any fair coin and flip it 12 times. Count the number of heads out of the 12 flips. This is your first sample. Do this 4 more times and count the number of heads out of the 12 flips in each sample. Thus, you should have 5 samples of 12 flips each. The important number is the number of heads in each sample...