Suppose a researcher decided to test a hypothesis that adding compost to tomato plants increases mean tomato mass. She knew the standard deviation of the mass of all tomato plants, so she chose a one-sample ?z‑test using a simple random sample of 50 plants that received compost. She used a significance level of ?=0.05α=0.05. The power of her test to detect a difference in mean tomato mass of 25 g or more was 0.98. What is the probability, ?β, that the researcher will make a type II error and fail to conclude that adding compost increases mean tomato mass when, in fact, adding compost increases mean tomato mass by 25 g or more? Give your answer as a decimal, precise to two decimal places.

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