Question

Score: 9 09%, 1 of 11 Score: 0 of 1 pt 9 of 11 (2 complete) 10.3.33-T Question, Heip Suppose the mean IQ score of people in a cetain country is 103 Suppose the director of a college obains a simple random saple of 42 students from that country and inds the mean Q is 107 8 with a standard deviation of 137 Complete parts (a) through (d) below (a)Conder ee hypoteses, p:103 versus H, μ>103 Explain what the actoristesing Perform te test at terdosenl of signifcance vote a condusion Ir teet Explain what the director is testing Choose the coect anbl Thedrnetor is testing t ts sample geevided suhirt evidence that the populaion neanla score is actally igualte 100 The drector is wig i th sample provided sofficient evidene that the population mean 1Q score is actualy not gealer than 103 The drectar ia testing &the sample provided suiclest evidance that the population mean Q scoe is achually not equal to 10 The drecor i samle v suficent vience thth potionan 1Q score is aly greater than 10 nd the test stac for this ypothesis tes

Answer 1

Solution :

$\mu$= 103

$\bar x$ = 107.8

S = 13.7

n = 42

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 103

H_a : $\mu$ > 103

Test statistic = T

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

= (107.8-103) /13.7 / $\sqrt$ 42

= 2.27

P(z > 2.27) = 1 - P(z < 2.27) = 0.0142

P-value = 0.0142

$\alpha$ = 0.05  

p = 0.0142 < 0.05, it is concluded that the null hypothesis is rejected..

There is enough evidence to claim that the population mean μ is greater than 103, at the 0.05 significance level.