Using the data below and a 0.05 significance level, test the claim that the responses occur with percentages of 15%, 20%, 25%, 25%, and 15% respectively. Select the correct conclusion about the null hypothesis.
Response: A, B, C, D, E
Frequency: 12, 15, 16, 18, 19
A) Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.
B) Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.
C) Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.
D) Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.
A) Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.
Using the data below and a 0.05 significance level, test the claim that the responses occur with percentages of 15%, 20%, 25%, 25%, and 15% respectively. Select the correct conclusion about the null hypothesis.
Response: A, B, C, D, E
Frequency: 12, 15, 16, 18, 19
A) Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.
B) Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.
C) Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.
D) Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.
A) Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.
Using the data below and a 0.05 significance level, test the claim that the responses occur with percentages of 15%, 20%, 25%, 25%, and 15% respectively. State the null hypothesis and the alternative hypothesis.
Response: A, B, C, D, E
Frequency: 12, 15, 16, 18, 19
A) H0: The responses do not occur with equal percentages, H1: The responses occur with equal percentages.
B) H0: The responses occur according to the stated percentages, H1: The responses do not occur with equal percentages.
C) H0: The responses occur with equal percentages, H1: The responses do not occur with equal percentages.
D) H0: The responses do not occur according to the stated percentages, H1: The responses occur according to the stated percentages.
C) H0: The responses occur with equal percentages, H1: The responses do not occur with equal percentages.
A company manager wishes to test a union leader's claim that employee absences occur on different weekdays with the same frequencies. Test the claim at a 0.05 level of significance if the following sample data have complied. State the null hypothesis and the alternative hypothesis.
Day: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday
Absences: 37, 15, 12, 23, 43
A) H0: The mean number of absences is all the same, H1: The mean number of absences is not all the same.
B) H0: The proportions of absences are greater for Monday and Friday, H1: The proportions of absences are all the same.
C) H0: The proportions of absences are all the same, H1: The proportions of absences are not all the same.
D) H0: The proportions of absences are not all the same, H1: The proportions of absences are all the same.
C) H0: The proportions of absences are all the same, H1: The proportions of absences are not all the same.
In studying the responses to a multiple-choice test question, the following sample data were obtained. At the 0.05 significance level, test the claim that the responses occur with the same frequency. State the null hypothesis and the alternative hypothesis.
response: A, B, C, D, E
frequency: 12, 15, 16, 18, 19
A) H0: The proportions of responses are not all equal, H1: The proportions of responses are all equal.
B) H0: The responses are all equal, H1: The responses are not all equal.
C) H0: The median number of responses are all equal, H1: The mean number of responses are all equal.
D) H0: The proportions of responses are all equal, H1: The proportions of responses are not all equal.
D) H0: The proportions of responses are all equal, H1: The proportions of responses are not all equal.
To test the claim, we will use the chi-square goodness-of-fit test. This test is appropriate when we want to compare the observed frequencies in a sample to the expected frequencies based on a specific distribution or set of proportions.
To find the expected frequencies, we first need to calculate the total number of responses. In this case, the total is 12 + 15 + 16 + 18 + 19 = 80.
Next, we calculate the expected frequency for each response category by multiplying the total number of observations (80) by the respective expected percentage. For example, the expected frequency for "A" is 80 * 0.15 = 12.
The expected frequencies for each response are:
A: 12
B: 16
C: 20
D: 20
E: 12
Now we can perform the chi-square goodness-of-fit test. The null hypothesis (H0) assumes that the observed frequencies follow the expected distribution. The alternative hypothesis (H1) assumes that the observed frequencies do not follow the expected distribution.
To calculate the chi-square test statistic, we use the formula:
χ² = Σ [(Observed - Expected)² / Expected]
Let's calculate the chi-square test statistic:
χ² = [(12-12)²/12] + [(15-16)²/16] + [(16-20)²/20] + [(18-20)²/20] + [(19-12)²/12]
= [0²/12] + [(-1)²/16] + [(-4)²/20] + [(-2)²/20] + [7²/12]
= 0 + 0.0625 + 0.4 + 0.1 + 4.83
≈ 5.3925
To determine the p-value associated with this test statistic, we need to refer to the chi-square distribution table or use software to calculate it. With a significance level of 0.05 and four degrees of freedom (five response categories - one), we find that the critical value of chi-square is approximately 9.488.
Since the calculated test statistic (5.3925) is less than the critical value (9.488), we fail to reject the null hypothesis. This means that there is not sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.
Therefore, the correct conclusion about the null hypothesis is option A) Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.