Question

Test the claim below about the mean of the differences for a population of paired data at the level of significance a. Assume the samples are random and dependent, and the populations are normally distributed. Claim: Ho<0; a=0.01. Sample statistics: d = 1.8, Sa = 3.4, n = 13 Identify the null and alternative hypotheses. Choose the correct answer below. 0 O B. Ho Hd < 0 Ha Ha 20 OD. Ho Hd = 0 O A. Ho Hd > 0 Ha Ha 50 Ho Hd 20 Ha Ho < 0 Ho Hd 50 Ha Ha > 0 Hai Moto OF. Ho Hd70 Ha Ha = 0 The test statistic is t=1 (Round to two decimal places as needed.) The critical value(s) is(are) to = (Round to two decimal places as needed. Use a comma to separate answers as needed.) Since the test statistic is the rejection region, the null hypothesis. There statistically significant evidence to support the claim.

Answer 1

The null and alternative hypotheses

Ho : $\large \mu$ d $\large \geq$ 0

H1 : $\large \mu$ d < 0

Test statistic

t = dbar /(Sd/√n)

t = 1.8/(3.4/√13)

t = 1.91

tcritical t0 for a = 0.01 , d.f = n -1= 12

to = t_{​​​​​​0.01,12} = 2.681

to = 2.68

Since the test statistic is lies in rejection region , fail to reject the null hypothesis . There is no statistically significant evidence to support the claim.