Question

A person claims to be able to make make a fair coin land heads more often...

A person claims to be able to make make a fair coin land heads more often than expected, using the power of telekenesis. A skeptical scientist investigates this claim and tosses a fair coin 75 times. It lands heads 41 times. Is there evidence to support the person’s claims?

(a) State a sensible null hypothesis

(b) State the precise definition of p-value and explain what “more extreme” means in this context

(c) Is a one-sided or two-sided test needed? justify

(d) Using dbinom(), or otherwise, calculate a p-value and interpret.

(e) (harder) Calculate a p-value using the normal approximation and compare your answer with the exact binomial p-value above.

Notes:
• Show detailed working, including appropriate mathematical notation for each question. For most questions this will involve showing your working from R or R Studio, (e.g. cut-and-paste commands and output from an R session).

• Any question involving regression will score 0 marks unless a scattergraph is produced.

• No Additional Info provided

Homework Answers

Answer #1

(a) The hypothesis being tested is:

H0: p = 0.5

Ha: p > 0.5

(b) In statistical hypothesis testing, the p-value or probability value is the probability of obtaining test results at least as extreme as the results actually observed, assuming that the null hypothesis is correct.

(c) This is a one-sided test because we have a direction.

(d) 0.09222417

(e) p-value = 0.2094617

Since the p-value (0.2094617) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that p > 0.5.

The R code is:

dbinom(41,75,41/75)
x = 41
n = 75
mu = 75*0.5
sd = sqrt(75*0.5*0.5)
z = (x - mu)/sd
pnorm(z, lower.tail = FALSE)

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Fair Coin? A coin is called fair if it lands on heads 50% of all possible...
Fair Coin? A coin is called fair if it lands on heads 50% of all possible tosses. You flip a game token 100 times and it comes up heads 42 times. You suspect this token may not be fair. (a) What is the point estimate for the proportion of heads in all flips of this token? Round your answer to 2 decimal places. (b) What is the critical value of z (denoted zα/2) for a 99% confidence interval? Use the...
Judy wants to test whether a coin is fair or not. Suppose she observes 477 heads...
Judy wants to test whether a coin is fair or not. Suppose she observes 477 heads in 900 tosses. Perform an appropriate p-value test using a 10% level of significance, and state your decision and conclusion.
Your friend claims he has a fair coin; that is, the probability of flipping heads or...
Your friend claims he has a fair coin; that is, the probability of flipping heads or tails is equal to 0.5. You believe the coin is weighted. Suppose a coin toss turns up 15 heads out of 20 trials. At α = 0.05, can we conclude that the coin is fair (i.e., the probability of flipping heads is 0.5)? You may use the traditional method or P-value method.
A coin is called fair if it lands on heads 50% of all possible tosses. You...
A coin is called fair if it lands on heads 50% of all possible tosses. You flip a game token 100 times and it comes up heads 61 times. You suspect this token may not be fair. (a) What is the point estimate for the proportion of heads in all flips of this token? Round your answer to 2 decimal places. (b) What is the critical value of z (denoted zα/2) for a 90% confidence interval? Use the value from...
You flip a fair coin N=100 times. Approximate the probability that the proportion of heads among...
You flip a fair coin N=100 times. Approximate the probability that the proportion of heads among 100 coin tosses is at least 45%. Question 4. You conduct a two-sided hypothesis test (α=0.05): H0: µ=25. You collect data from a population of size N=100 and compute a test statistic z = - 1.5. The null hypothesis is actually false and µ=22. Determine which of the following statements are true. I) The two-sided p-value is 0.1336. II) You reject the null hypothesis...
Using R or R-studio. 3. A fair coin is tossed until the first head occurs. Do...
Using R or R-studio. 3. A fair coin is tossed until the first head occurs. Do this experiment T = 10; 100; 1,000; 10,000 times in R, and plot the relative frequencies of this occurring at the ith toss, for suitable values of i. Compare this plot to the pmf that should govern such an experiment. Show that they converge as T increases. What is the expected number of tosses required? For each value of T, what is the sample...
If you flip a fair coin, the probability that the result is heads will be 0.50....
If you flip a fair coin, the probability that the result is heads will be 0.50. A given coin is tested for fairness using a hypothesis test of H0:p=0.50H0:p=0.50 versus HA:p≠0.50HA:p≠0.50. The given coin is flipped 240 times, and comes up heads 143 times. Assume this can be treated as a Simple Random Sample. The test statistic for this sample is z= The P-value for this sample is If we change the significance level of a hypothesis test from 5%...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT