Due in 3 hours, 26 minutes. Due Sun 03/25/2018 3:59 am Show Intro Instructions A

Question

Due in 3 hours, 26 minutes. Due Sun 03/25/2018 3:59 am Show Intro Instructions According to a report issued by the CDC i 2013. 668 % of women 40 years of age and over had a ma nno ran within the last two years An oncologist at the CDC would like know if there has been a change in this percentage over the last two years. A random sample of 717 women (40 and older) is taken, and each is asked the date of their last mammogram . Verify that the assumptions bave been satisfied to conduct a hypothesis test, Random sample? Select an answer v1 . The variable recorded was: Select an answer and n(1 -p) Both of the values are greater than 10: 1 Select an answer V) It was found that 492 women in the sample had a mammogram in the last two years. Test the approperiate hypotheses using a significance level of . Ho: Select an answer Ha Select an answer decision rule: reject Ho if probabilitya . Test Statistic: z - round the -score to two decimal places - cary at least four decinal places throughout all of your calculations) . probability (Note: round the probability to four decimal places) Decision: Select an answer Conclusion: At the 0.01 level, there Select an answerl is select an answer 66.8%. significant evidence to conclude the to conclude the percentage of women 40 or older who have had a mammogram in the last two years

Explanation / Answer

Solution:-

Random sample - Yes

The variable recorded was women 40 years of age and over had a mammogram within last two years.

np = 0.668 × 717 = 478.96

n(1-p) = 0.332 × 717 = 238.04

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.668
Alternative hypothesis: P 0.668

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.01759
z = (p - P) /

z = 1.034

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than -1.034 or greater than 1.034.

Thus, the P-value = 0.3011

Interpret results. Since the P-value (0.3011) is greater than the significance level (0.01), we cannot reject the null hypothesis.

At the 0.01 level, there is not significant evidence to conclude the percentage of women 40 or older who have had a mammogram in the last two years is not 66.8%.

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