Question

It is claimed that the mean of a population is 67. A random sample was obtained and is represented by data labelled “problem 9”. Complete the hypothesis test with α=5%. Use p-value method.

49.5
69.3
80.5
81.9
70
62.2
76.7
92.4
92.7
70.9
95.5
62.5
69.1
70.9
79.6
68.4
88
52.3
95.5
85.8
61.2
98.1
100.1
68.8
76.3
66.9
103.2
79.8
60.1
37.3
55.3
83.6
83.7
76.9
71.6
67.6
69.9
80.9
102.2
85.1

Answer 1

Calculation
	x	x-mean	(x-mean)2
	49.5	-26.5575	705.3008063
	69.3	-6.7575	45.66380625
	80.5	4.4425	19.73580625
	81.9	5.8425	34.13480625
	70	-6.0575	36.69330625
	62.2	-13.8575	192.0303063
	76.7	0.6425	0.41280625
	92.4	16.3425	267.0773063
	92.7	16.6425	276.9728063
	70.9	-5.1575	26.59980625
	95.5	19.4425	378.0108063
	62.5	-13.5575	183.8058063
	69.1	-6.9575	48.40680625
	70.9	-5.1575	26.59980625
	79.6	3.5425	12.54930625
	68.4	-7.6575	58.63730625
	88	11.9425	142.6233063
	52.3	-23.7575	564.4188063
	95.5	19.4425	378.0108063
	85.8	9.7425	94.91630625
	61.2	-14.8575	220.7453063
	98.1	22.0425	485.8718063
	100.1	24.0425	578.0418062
	68.8	-7.2575	52.67130625
	76.3	0.2425	0.05880625
	66.9	-9.1575	83.85980625
	103.2	27.1425	736.7153063
	79.8	3.7425	14.00630625
	60.1	-15.9575	254.6418063
	37.3	-38.7575	1502.143806
	55.3	-20.7575	430.8738063
	83.6	7.5425	56.88930625
	83.7	7.6425	58.40780625
	76.9	0.8425	0.70980625
	71.6	-4.4575	19.86930625
	67.6	-8.4575	71.52930625
	69.9	-6.1575	37.91480625
	80.9	4.8425	23.44980625
	102.2	26.1425	683.4303063
	85.1	9.0425	81.76680625
sum=	3042.3		8886.19775
mean=	76.0575		222.1549438
	variance=	222.155
	standard deviation=	sqrt(222.155)
	standard deviation=	14.90486309

Given = 67 population mean , level =5%

We have n=40 , = 76.0575 , S= 14.9048

here sample size is large so we can use Z test

Null hypothesis H0: = 67

H1: 67 two tailed alternative

Test statistics   

  

The P-Value is 0.00012

Decision : The P-Value (0.00012) < 0.05

   so Reject Ho

Conclusion: We conclude that the claim that the mean of a population is 67 is not true