Question

You may need to use the appropriate technology to answer this question. Consider the following hypothesis test. Hou 55 H: 4 < 55 A sample of 35 is used. Identify the p-value and state your conclusion for each of the following sample results. Use a = 0.01. (a) = 54 and 5 = 5.2 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject Ho. There is insufficient evidence to conclude that u < 55. Reject Ho. There is sufficient evidence to conclude that u < 55. O Do not reject Ho. There is insufficient evidence to conclude that u < 55. O Do not reject Ho. There is sufficient evidence to conclude that u < 55. (b) * = 53 and 5 = 4.7 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject Ho. There is insufficient evidence to conclude that u < 55. Reject Ho. There is sufficient evidence to conclude that u < 55. Do not reject Ho. There is insufficient evidence to conclude that u < 55. O Do not reject Ho. There is sufficient evidence to conclude that u < 55. (c) = 56 and 5 = 6.0 Find the value of the test statistic. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject Ho. There is insufficient evidence to conclude that u < 55. Reject Ho. There is sufficient evidence to conclude that u < 55. Do not reject Ho. There is insufficient evidence to conclude that u < 55. Do not reject Ho. There is sufficient evidence to conclude that u < 55.

Answer 1

As the population standard deviation is not we will use t distribution in all test.

a.Test statistic:

$t = \frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}=\frac{54-55}{\frac{5.2}{\sqrt{36}}}=-1.154$

d.f. = n-1= 36-1= 35

P-value for one tailed t test with test statistic -1.154 wif d.f. (35) by Excel formula=TDIST(1.154,35,1)=0.128

As P-value(0.128) is greater than alpha(0.01) we fail to reject the null hypothesis.

So answer is

Do not reject Ho. There is insufficient evidence to conclude that u < 55.

b.

$t = \frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}=\frac{53-55}{\frac{4.7}{\sqrt{36}}}=-2.553$

d.f.=36-1=35

P-value for one tailed t test with test statistic -2.553 with d.f. (35) by Excel formula=TDIST(2.553,35,1)=0.008

As P-value(0.008) is less than alpha(0.01) we reject the null hypothesis.

So the answer is

Reject Ho. There is sufficient evidence to conclude that u < 55.

c

$t = \frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}=\frac{56-55}{\frac{6}{\sqrt{36}}}=1$

P-value for one tailed t test with test statistic 1 with d.f. (35) by Excel formula=TDIST(1,35,1)=0.162

As P-value(0.162) is greater than alpha(0.01) we fail to reject the null hypothesis.

so the answer is