Question

The following dataset contains a random sample of lifetime of 120 BMW Xenon headlight bulbs. The manufacturer of these bulbs wants to know whether it can claim that the bulbs last more than 1000 hours. Use a=0.01

93	1053.74
94	1032.37
95	1003.42
96	908.74
97	1037.92
98	1096.83
99	1169.07
100	842.85
101	1038.22
102	973.30
103	996.08
104	984.70
105	989.44
106	1023.07
107	1047.95
108	1073.63
109	1021.51
110	977.27
111	928.44
112	910.28
113	990.68
114	1043.82
115	1038.36
116	1023.51
117	1026.85
118	987.21
119	1053.35
120	1077.91

a)Formulate the hypotheses.

b)What is the value of the test statistic?

c)What are the critical values of the test?

d)Find the p-value of the test.

e)What is your conclusion? Explain it in the context of the problem.

Answer 1

(a) The hypothesis of the test

H0: Mean time of the bulb last will not be greater than 1000 Hours

H1: Mean time of the bulb last will be greater than 1000 Hours

(b) The value of the test statistic t = 0.7743

(c) The critical value of the test statistic t-critical = 2.479

(d) The p value of the test is = 0.4455

(e) As we found the p value is 0.4455, which is greater than the level of significance alpha = 0.01, therefore we fail to reject the null hypothesis and concluded that the mean time of the bulb last will not be greater than 1000 hours for the given data set.

Note: I am attaching all the output of the statistical test.