Question

# A large drug store chain outsources the manufacturing of its pain relief tablets to two different...

A large drug store chain outsources the manufacturing of its pain relief tablets to two different independent manufacturers, Manufacturer A and Manufacturer B. The quality control department of the chain would like to ensure that the population mean amount of the active ingredient in the tablets is still the same between the two manufacturers. The department assumes the population standard deviation for the amount of the active ingredient in a tablet based on the specifications from the manufacturers. The quality control department selects a random sample of tablets from each manufacturer across dozens of lots. The tablets are then analyzed using chromatography to determine the amount of the active ingredient in each tablet. The results of the analysis and the population standard deviations that are assumed for this hypothesis test are provided in the table below. Let μ1 be the population mean amount of the active ingredient, in milligrams, in tablets produced by Manufacturer A and μ2 be the population mean amount of the active ingredient, in milligrams, in tablets produced by Manufacturer B. If the test statistic is z=−1.65, what is the p-value for this hypothesis test?

 z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.03 0.029 -1.7 0.045 0.044 0.043 0.042 0.041 0.04 0.039 0.038 0.038 0.037 -1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046 -1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 -1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068 -1.3 0.097 0.095 0.093 0.092 0.09 0.089 0.087 0.085 0.084 0.082 -1.2 0.115 0.113 0.111 0.109 0.107 0.106 0.104 0.102 0.1 0.099 -1.1 0.136 0.133 0.131 0.129 0.127 0.125 0.123 0.121 0.119 0.117

For z = -1.65 the cooresponding p-value is 2*0.049 = 0.098

Explanation: p-value using table given :

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