Question

A group of students estimated the length of one minute without reference to a watch or​ clock, and the times​ (seconds) are listed below. Use a 0.10 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one​ minute?

81

91

49

74

48

34

68

70

77

54

71

82

104

99

76

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Question: Listed below are the lead concentrations in μ​g/g measured in different traditional medicines. Us...

Listed below are the lead concentrations in μ​g/g measured in different traditional medicines. Use a 0.01 significance level to test the claim that the mean lead concentration for all such medicines is less than 16 μ​g/g.

12  2.5  15.5  18  18.5  5  22  10  13  13.5

A group of students estimated the length of one minute without reference to a watch or​ clock, and the times​ (seconds) are listed below. Use a 0.10 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one​ minute?

81

91

49

74

48

34

68

70

77

54

71

82

104

99

76

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those​ tests, with the measurements given in hic​(standard head injury condition​ units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified​requirement?

719  657  1021  559  516  500

Answer 1

a)

= 0.10

sample size (n) = 15

sample mean = 71.87

sample standard deviation (S) = 19.33

Hypothesis:

Test statistic:

Degrees of Freedom = n-1 = 15-1 = 14

P-value: 0.032 ..............................From t table

Conclusion:

P-value < , i.e. 0.032 < 0.10, That is Reject Ho at 10% level of significance.

b)

= 0.01

sample size (n) = 10

sample mean = 13

sample standard deviation (S) = 6.03

Hypothesis:

Ho: = 16

Ha: < 16

Test statistic:

Degrees of Freedom = n-1 = 10-1 = 9

P-value: 0.075   ........................From t table

Conclusion:

P-value > , i.e. 0.075 < 0.01, That is Fail to Reject Ho at 1% level of significance.

Therefore, there is Not enough evidence to support the claim that the mean lead concentration for all such medicines is less than 16 μ​g/g.