How do you know if a $p$-value is statistically significant?

An archer claims that her skill at firing arrows is such that she can hit the bullseye $40\%$ of the time. A hypothesis test at the $5\%$ significance level is carried out to test if the archer is as good as she claims to be. The archer fires $12$ arrows at a target.

Find the rejection region.

A television channel claims that $25\%$ of its programmes are nature programmes. Yolande thinks the percentage claimed is too high. To test her hypothesis, she chooses $20$ programmes at random.

If there are only two nature programmes, calculate the test statistic. What conclusion does Yolande reach? Significance level is $10\%$.

For testing $H_0:\mu ={\mu }_0$ Against $H_1:\mu <{\mu }_0$, what is the critical value at $\alpha =0.01$.

A manufacturer sells bags of $20$ marbles in mixed colours. It claims that $30\%$ of the marbles are red. Ginny thinks this is incorrect and tests the claim by opening a bag of marbles and counting how many are red.

Carry out a hypothesis test at the $10\%$ level of significance given that Ginny finds three red marbles.

Suppose Ginny thinks the percentage should be lower than $30\%$. State the hypotheses. Will Ginny's conclusion change?

A farmer finds that $30\%$ of his sheep are deficient in a particular mineral. He changes their feed and tests $80$ sheep to find out if the number has decreased.

Using a suitable approximating distribution, carry out a hypothesis test at the $10\%$ significance level given that $19$ of the sheep are mineral deficient.

Critical value at $5\%$ level of significance for two-tailed large sample test is

A television channel claims that $25\%$ of its programmes are nature programmes. Yolande thinks the percentage claimed is too high. To test her hypothesis, she chooses $20$ programmes at random.

If there are only two nature programmes, calculate the test statistic. If the significance level was $5\%$, what conclusion would Yolande reach?

Critical value at $5\%$ level of significance for two-tailed large sample test is

A supplier of duck hatching eggs claims that up to $80\%$ of its duck eggs will produce ducklings. Gareth orders $16$ duck hatching eggs and carries out a hypothesis test at the $10\%$ significance level to test this claim.

Find the rejection region.

For testing $H_0:\mu ={\mu }_0$ Against $H_1:\mu <{\mu }_0$, what is the critical value at α = 0.01

A manufacturer sells bags of $20$ marbles in mixed colours. It claims that $30\%$ of the marbles are red. Ginny thinks this is incorrect and tests the claim by opening a bag of marbles and counting how many are red.

Carry out a hypothesis test at the $10\%$ level of significance given that Ginny finds three red marbles. Find the critical value for this test.

To test the claim that a coin is biased towards tails, it is flipped nine times. Tails appears seven times.

test at the $5\%$ significance level whether the claim is justified.