Question

1 a guy is presented with 400 cards face down and is asked to determine which of the four symbols (star, circle, square, triangle) is on the card. He was correct in 112 of these cases. What proportion correct did he get in the experiment? Express as a decimal to two places.Then construct a 99% confidence interval for p, please show work. finally, Solve for test statistic is Ho p=0.25 and Ha is p>0.25

Answer 1

Solution :

Given that,

n = 400

x = 112

Point estimate = sample proportion = = x / n = 112 / 400 = 0.280

1 - = 1 - 0.280 = 0.720

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 ((0.280 * (0.720) / 400)

= 0.058

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.280 - 0.058 < p < 0.280 - 0.058

0.222 < p < 0.0338

The 99% confidence interval for the population proportion p is : ( 0.222 , 0.338 )

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.25

Ha : p > 0.25

n = 400

x = 112

= x / n = 112 / 400 = 0.28

P0 = 0.25

1 - P0 = 1 - 0.25 = 0.75

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.28 - 0.25 / [0.25(0.75) / 400]

= 1.386

P(z > 1.386) = 1 - P(z < 1.386 ) = 1 - 0.9171 = 0.0829

P-value = 0.0829

= 0.05    

0.0829 > 0.01

P-value >

Fail to reject the null hypothesis .