The signal strengths, measured in decibel-milliwatts (dBm), were recorded for two competing IoT transmission protocols within a smart city grid. A random sample of 80 transmission points using Protocol X yielded a mean signal strength of −53.2-53.2−53.2 dBm with a standard deviation of 3.83.83.8 dBm. A second independent random sample of 120 transmission points using Protocol Y yielded a mean signal strength of −51.5-51.5−51.5 dBm with a standard deviation of 4.64.64.6 dBm.
Test, at the 1% level of significance, whether the mean signal strength of Protocol X is lower than the mean signal strength of Protocol Y. State your hypotheses clearly.
State two assumptions required for the validity of the hypothesis test performed in part (a).
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.