Test the following hypotheses for a multinomial probability distribution by using the goodness of fit test.

H0: PA = .40, PB = .40, and PC = .20
H0: The probabilities are not PA = .40, PB = .40, and PC = .20

A sample of size 200 yielded 60 in category A, 120 in category B, and 20 in category C. Use = .01 and test to see whether the probabilities are as stated in H0. If answer is zero enter "0".

a. Use the p-value approach.
Test statistic = (to 0 decimals)
p-value = (to 3 decimals)

- Select your answer -Reject the null hypothesisDo not reject the null hypothesisItem 3

b. Repeat the test using the critical value approach (to 3 decimals).

Reject H0 if

Listed below are time intervals (min) between eruptions of a geyser. assume that the "recent" times are within the past few years, the "past" times are from around 20 years ago, and that the two samples are independent simple random samples selected from normally distributed populations. do not assume that the population standard deviations are equal. does it appear that the mean time interval has changed? is the conclusion affected by whether the significance level is 0.10 or 0.01? recent 78 90 90 79 57 101 62 87 71 87 81 84 57 80 74 103 62 past 88 89 93 94 65 85 85 92 87 91 89 91 follow the steps of hypothesis testing, including identifying the alternative and null hypothesis, calculating the test statistic, finding the p-value, and making a conclusions about the null hypothesis and a final conclusion that addresses the original claim. use a significance level of 0.10. is the conclusion affected by whether the significance level is 0.10 or 0.01? answer choices below: a) yes, the conclusion is affected by the significance level because h0 is rejected when the significance level is 0.01 but is not rejected when the significance level is 0.10. b) no, the conclusion is not affected by the significance level because h0 is not rejected regardless of whether a significance level of 0.10 or 0.01 is used. c) yes, the conclusion is affected by the significance level because h0 is rejected when the significance level is 0.10 but is not rejected when the significance level is 0.01. d) no, the conclusion is not affected by the significance level because h0 is rejected regardless of whether a significance level of 0.10 or 0.01 is used.