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).
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.