Question

odle x | G 2 325 featherstone x Maren Morris ← × | v BA 3400003 Onlin Mind Tap . Cen nb/ui/evo/indexhtmielSBN 97813371153778d-4264466188snapshotld-10558738 TAP signment Consider the follewing hypothesis test: He: μ-16 A sample of 40 provided a sample mean of 14.19. The population standard deviation is 6. Enter negative value as negative number. a. Compute the value of the test statistic (to 2 decimals) 1.91 8 b. What is the p-value (to 4 decimais)? Use the value of the test statistic rounded to 2 deomal places in your calculations c. Using a-0.05, can it be concluded that the population mean is not equal to 16 03 O Answer the next three questions using the critical value appreach. d.Using α-0.05, what are the rocal values for the test stabsbe? (+ or-) (o 2 decima's) Stata he revection n:RetH eteur Can it be concluded that the population mean is not equal to 16? the loer critical value and iseledtou uoper critical value.

Answer 1

We have

n=40,  $\bar{x}$ =14.19, s =6 and $\mu$ =16

The t- statistics is given by

$t = \frac{\bar{x} - \mu}{s/\sqrt{n}}$

a)

$t = \frac{1 4.19- 16}{6/\sqrt{40}}$

= - 1.9079 = -1.91

b)

From t- table for t= -1.91 and df =40-1 = 39

p- value = 0.0638

c) At $\alpha$=0.05, since p- value is > 0.05 so we accept the null hypothesis. We can conclude that population mean is equal to 16.

d) For $\alpha$ =0.05 and df =39 the critical value is +/- 2.02.

Since t< +/-2.02, hence we accept null hypothesis.