Question

Consider the observed frequency distribution for the set of random variables on the right. a. Perform a​ chi-square test using alphaequals0.05 to determine if the observed frequencies follow the binomial probability distribution when pequals0.50 and nequals4. b. Determine the​ p-value and interpret its meaning. Random​ Variable, x ​Frequency, fo 0 18 1 106 2 154 3 106 4 16 Total 400 a. State the appropriate null and alternative hypotheses. Choose the correct answer below. A. Upper H 0​: The mean number of the random variable is equal to 0. Upper H 1​: The mean number of the random variable is less than 0. B. Upper H 0​: The mean number of the random variable is equal to 0. Upper H 1​: The mean number of the random variable is not equal to 0. C. Upper H 0​: The distribution of the random variable is binomial with nequals4 and pequals0.50. Upper H 1​: The distribution of the random variable is not binomial with nequals4 and pequals0.50. D. Upper H 0​: The distribution of the random variable is not binomial with nequals4 and pequals0.50. Upper H 1​: The distribution of the random variable is binomial with nequals4 and pequals0.50. The​ chi-square test statistic is chi squaredequals nothing. ​(Round to two decimal places as​ needed.) The​ chi-square critical value is chi Subscript alpha Superscript 2equals nothing. ​(Round to three decimal places as​ needed.) Determine the proper conclusion. Choose the correct answer below. A. Do not reject the null hypothesis. There is not enough evidence to conclude that the random variable does not follow a binomial probability distribution with nequals4 and pequals0.50 . B. Reject the null hypothesis. There is not enough evidence to conclude that the random variable does not follow a binomial probability distribution with nequals4 and pequals0.50 . C. Reject the null hypothesis. There is enough evidence to conclude that the random variable does not follow a binomial probability distribution with nequals4 and pequals0.50. D. Do not reject the null hypothesis. There is enough evidence to conclude that the random variable does not follow a binomial probability distribution with nequals4 and pequals0.50. b.​ p-valueequals nothing ​(Round to three decimal places as​ needed.) State the appropriate conclusion. ▼ Do not reject Reject the null hypothesis because the​ p-value is ▼ less than greater than alpha. There is ▼ insufficient sufficient evidence to conclude that the observed frequency distribution does not follow a binomial probability distribution.

Answer 1