Part CCSIR NET December 2025the-discrete-binomial-rejection-region-jumps-from-size-0-063-at-k-6-to-0-008-at-k-7-there-is-no-level-exactly-0-05

The discrete binomial rejection region jumps from size 0 063 at k 6 to 0 008 at k 7 there is no level exactly 0 05

Let $X_{1},X_{2},\dots,X_{7}$ be a random sample drawn from a continuous distribution with unknown unique median M. The null hypothesis $H_{0}:M=2$ is tested against the alternative $H_{1}:M>2$ at level of significance 0.05 using the right-tailed test based on the Sign test statistic K, which is the number of observations in the sample greater than 2. If the observed sample is −3,−6,1,9,4,10,12, which of the following statements are true?

A. $H_{0}$ is rejected
B.The p-value of the test is greater than 0.01✓
C.Under $H_{0}, E(K) = 3.5$ ✓
D.If $X_{(i)}$ denotes the i-th smallest observation of the sample, then $[X_{(2)},X_{(6)}]$ is a confidence interval for M with confidence coefficient at least 0.95

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: A UMP test exists for every testing problem

The discrete binomial rejection region jumps from size 0 063 at k 6 to 0 008 at k 7 there is no level exactly 0 05

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