Amanufacturer of colored candies states that 13% of the candies in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. a student randomly selected a bag of colored candies. he counted the number of candies of each color and obtained the results shown in the table. test whether the bag of colored candies follows the distribution stated above at the α=0.05 level of significance. color | frequency | claimed proportion brown | 60 | 0.13 yellow | 65 | 0.14 red | 56 | 0.13 blue | 63 | 0.24 orange | 82 | 0.20 green | 63 | 0.16

The null and alternative hypotheses are:

The bag of colored candies follows the distribution stated

The bag of colored candies does not follow the distribution stated

Under the null hypothesis, the test statistic is:

Where:

is the observed frequencies

is the expected frequencies

The calculation are done in the attachment

Now, we have to find the chi-square critical value at 0.05 significance level for df = n - 1 = 6 - 1 = 5. Using the chi-square table, we have:

Since, the chi-square test statistic is greater than chi-square critical value. Therefore, we reject the null hypothesis and conclude that the bag of colored candies does not follow the distribution stated.

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.