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).
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.