Question

7.3.23-T Question Help Test a claim that the mean amount of carbon monoxide in the air in U.S. cities is less than 2.33 parts per million. It was found that the mean amount of cartxon monoxide in the air for the random sample of 64 cities is 2.38 parts per million and the standard deviation is 2.09 parts per million. At a=0.01, can the daim be supported? Complete parts (a) through (e) below. Assume the population is normally distributed. (a) Identify the claim and state Ho and H. Which of the following correctly states Ha and H.? Hp 2 2.38 Hau < 2.38 (Type Integers or decimals. Do not round.) The clairn is the alternative hypothesis. (b) Use technology to find the critical value(s) and identify the rejection region's). The critical value(s) is/are to - (Use a comma to separate answers as needed. Round to two decimal places as needed.) Enter your answer in the answer box and then click Check Answer 4 parts 4 remaining Clear All Check Answer

(b) Use technology to find the critical​ value(s) and identify the rejection​ region(s).

(c) Find the standardized test​ statistic, t.

​(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.

Answer 1

Based on the given details of the sample and population sample mean is Xˉ=2.38 and the sample standard deviation is s = 2.09.

a) The hypotheses are:

| Ho: 2.33 Ha: μ< 2.33

So, the Alternate hypothesis is the claim.

b) The given 0.05 level of significance and sample size = 64 so, the degree of freedom = n-1= 64-1=63.

So, the critical value is calculated using the excel formula for T-distribution which is =T.INV(0.01,63) so, the critical value is tc= -2.39.

Rejection region:

reject Ho if t <tc

c) The test statistic is calculated as:

+-X - Mo_2.38 - 2.33 t=3/ vn2.09/164 = 0.191

d) Decision:

SInce Text statistic is greater than t_c hence we fail to reject the null hypothesis.

P-value:

The P-value is calculated using excel formula =T.DIST(0.191,63,TRUE), results in P-value = 0.5756.

e) Conclusion:

Since P-value is greater than 0.01 and t is greater than -2.39, hence we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim.