Question

а. Use the data given to test the following hypotheses Но : и <1,200 x 1,216, n 111, o = 110, a = 0.10 1,200 Ha Round your answer to 2 decimal places. and wi The value of the test statistic is reject the null hypothesis LINK TO TEXT fail to reject the null hypothesis

Answer 1

Solution :

$\mu$= 1200

$\bar x$ = 1216

$\sigma$ = 110

n = 111

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$  ≤ 1200

H_a : $\mu$ > 1200

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (1216-1200) / 110 / $\sqrt$ 111

= 1.532

Test statistic = z = 1.53

P(z > 1.53 ) = 1 - P(z < 1.53 ) = 1 - 0.937

P-value =0.0630

$\alpha$ = 0.10  

P-value < $\alpha$

0.063 < 0.10

Reject the null hypothesis .

There is sufficient evidence to suggest that   

b ) Given that,

$\mu$= 24

$\bar x$ = 27.3

$\sigma$ = 8..45

n = 55

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$  = 24

H_a : $\mu$   $\neq$ 24

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (27.3 -24) / 8..45 / $\sqrt$ 55

= 3.059

Test statistic = z = 3.06

P-value =0.002

$\alpha$ = 0.01

P-value < $\alpha$

0.002< 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that