Hypothesis Testing question

From a past A Level paper,

Question -

Before attending a basketball course, a player found that 60% of his shots made a score. After attending the course the player claimed he had improved. In his next game, he tried 12 shots and scored in 10 of them. Assuming shots to be independent, test this claim at the 10% significance level.

Please show me the possible methods (Binomial, Normal etc) which can be used. Thank you! =D

(Answers - (1)Using Binomial way, P=0.0834, Reject Ho, accept claim at 10%.
(2)Using Normal way, P=0.0877, Reject Ho, accept claim at 10%)

Quote:

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Originally Posted by agbrianlee355

From a past A Level paper,

Question -

Before attending a basketball course, a player found that 60% of his shots made a score. After attending the course the player claimed he had improved. In his next game, he tried 12 shots and scored in 10 of them. Assuming shots to be independent, test this claim at the 10% significance level.

Please show me the possible methods (Binomial, Normal etc) which can be used. Thank you! =D

(Answers - (1)Using Binomial way, P=0.0834, Reject Ho, accept claim at 10%.
(2)Using Normal way, P=0.0877, Reject Ho, accept claim at 10%)

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(1) Let X be the random variable number of shots scored out of 12.

$\displaystyle H_0:$ X ~ Binomial(n = 12, p = 0.6)

$\displaystyle H_1:$ X ~ Binomial(n = 12, p > 0.6)

$\displaystyle P = \Pr(X \geq 10 \, | \, H_0) = 0.0834$ using my TI-89.

Since the P-value is less than 0.1 (the level of significance) the null hypohesis is rejected.


(2) Use the normal approximation to the binomial distribution.