Question

Part 1) You wish to test the claim that μ = 40 at a level of significance of α = 0.05 and are given sample statistics n = 13, x ¯ = 52, and s = 16. Compute the value of the standardized test statistic, t. Round your answers to three decimal places.

Part 2)

Your company claims that 9 out of 10 doctors (i.e. 90%) recommend its brand of cough syrup to their patients. To test this claim against the alternative that the actual proportion is less than 90%, a random sample of 200 doctors was chosen which results in 174 who indicate that they recommend this cough syrup. Find the standardized test statistic, z. Round to two decimal places.

Answer 1

Solution :

1) = 40

= 52

s = 16

n = 13

This is the two tailed test .

The null and alternative hypothesis is

H0 :   =40

Ha : 40

Test statistic = t

= ( - ) / s / n

= (52 -40 ) /16 / 13

= 2.704

p(Z >2.704 ) = 1-P (Z < 2.704 ) = 0.0192

P-value = 0.0192

= 0.05  

0.0192 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that   

2)

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.90

Ha : p < 0.90

= x / n = 174/200 = 0.87

P0 = 0.90

1 - P0 = 1 -0.90 = 0.10

Test statistic = z

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

=0.87 -0.10 / [0.90*(0.10) /200 ]

= -1.41

P(z < -1.41) = 0.0793

P-value = 0.0793