A pharmaceutical company would like to investigate the response time of a COVID-19 rapid test. The company claims that the response time is 16 minutes. To investigate this claim, the company decided to consider the response time of a random sample of 20 tests. Given:  The response times has a normal distribution with a standard deviation of σ=2. The company wishes to test this claim at α=0.01 level of significance. The value of the test statistic is z=1.92   a) The sample mean is x¯=16.86. Construct a 99% confidence interval for the mean response time of a COVID-19 rapid test, by answering the following questions (Round answer to 4 decimal places): The margin of error is: _________  The confidence interval is: (_______ ;_________)   b) Calculate the p-value __________ The company may conclude that the response time _____ (differs/does not differ) from 16 minutes at α=0.01 level of significance c) The company would like to increase the sample size so that the sample mean is within 0.8 minutes of the true mean with 99% confidence. The new required sample size is ________

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