Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 27, 30, 46, 38, 28, 31. Use a 0.10 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? Click here to view the chi-square distribution table. The test statistic is (Round to three decimal places as needed.) The critical value is (Round to three decimal places as needed.) State the conclusion. Ho. There sufficient evidence to support the claim that the outcomes are not equally likely. The outcomes to be equally likely, so the loaded die to behave differently from a fair die.Chi-square distribution table Area to the Right of the Critical Value Degrees of Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.001 0.004 0.016 2.706 0.010 0.020 0.051 0.103 0.211 4.605 0.072 0. 115 0.216 0.352 0.584 6.251 0.207 0.297 0.484 0.711 1.064 7.779 0.412 0.554 0.831 1.145 1.610 9.236 0.676 0.872 1.237 1.635 2.204 10.645 0.989 1.239 1.690 2.167 2.833 12.017 1.344 1.646 2.180 2.733 3.490 13.362 1.735 2.088 2.700 3.325 4.168 14.684 10 2.156 2.558 3.247 3.940 4.865 15.987In an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts (a) through (c) below. Purchased Gum Kept the Money Students Given Four Quarters 33 12 Students Given a $1 Bill 18 35 a. Find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill. The probability is]. (Round to three decimal places as needed.) b. Find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill. The probability is (Round to three decimal places as needed.) c. What do the preceding results suggest? O A. A student given a $1 bill is more likely to have kept the money than a student given four quarters. O B. A student given a $1 bill is more likely to have spent the money than a student given four quarters. O C. A student given a $1 bill is more likely to have kept the money. O D. A student given a $1 bill is more likely to have spent the money.Households are randomly selected and partitioned into groups of four. For those groups, the random variable x is the number of households X P(x) with a printer. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a 0 0.029 probability distribution is not given, identify the requirements that are not satisfied. 1 0.144 2 0.334 3 0.357 4 0.136 Does the table show a probability distribution? Select all that apply. O A. Yes, the table shows a probability distribution. OB. No, not every probability is between 0 and 1 inclusive. O C. No, the sum of all the probabilities is not equal to 1. D. No, the numerical values of the random variable x are not associated with probabilities. O E. No, the random variable x is categorical instead of numerical. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. H= household(s) (Round to one decimal place as needed.) O B. The table does not show a probability distribution. Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. 6= household(s) (Round to one decimal place as needed.) O B. The table does not show a probability distribution