Question

In this article, researchers evaluated links between playing golf and the risk of stroke, heart attack, or death.

Golfing at least once a month may lower a person's risk of early death, according to new research presented on Wednesday at the American Stroke Association's International Stroke Conference 2020.
The sport, a favorite of presidents from Woodrow Wilson and Calvin Coolidge to Barack Obama, and Donald Trump is a gentle activity, with very few opportunities for high-intensity exercise.
But the study, by researchers at the University of Missouri, found any activity that gets older adults active and socializing monthly, weekly or daily is enough to reduce the risk of stroke and heart attack.
Researchers analyzed 10 years of data on 5,900 over-65-year-olds between 1989 and 1999, all of whom visited a clinic every six months.
They found that just 8.1% of the 384 golfers (people who golfed at least once a month) had strokes over the 10 years, compared to 15.1% of the non-golfers. Also, 9.8% of the golfers had heart attacks, compared to 24.6% of the non-golfers.
The results, the researchers said, are significant — but added it is also significant that golf is a sport that attracts wealthy people, who tend to have better healthcare and lower risks of strokes and heart attacks.
Some 25 million Americans play golf, which can reduce stress and offer an opportunity for regular exercise.
But that's not enough to satisfy the US Department of Health that they're getting real exercise: it is not on the government's list of sports that qualify as legitimate ways to work out.
Golf burns more calories than fishing or canoeing, but that is only for people playing without carts or caddies. It can even be played with a broken leg, as Tiger Woods did in 2009.
As such, golf has inspired fierce debates over whether it qualifies as a sport. Golf was even removed from the Olympic games for 112 years between 1904 and 2016.
"Golf isn't a sport; it's a skill much like bowling," lawyer Larry Atkins wrote in a controversial op-ed for The Chicago Tribune in 2002 after Tiger Woods won his third Masters. "It's an activity that older people take up when their knees go bad and they can't play real sports like basketball, baseball and football anymore."
For lead study author Adnan Qureshi, professor of neurology at the University of Missouri in Columbia, Missouri, the findings clearly show goal is beneficial.
"The US Department of Health and Human Services Physical Activity Guidelines for Americans does not yet include golf in the list of recommended physical activities," Qureshi said. "Therefore, we are hopeful our research findings could help to expand the options for adults to include golf."

1. Provide a null and one-tailed hypothesis for the association between playing golf and heart attacks and calculate a Z statistic and p value for your null and one-tailed hypotheses (4 points)

Answer 1

This is a very long detailed question. Therefore, let's break it down slowly. As per the question, there was a survey done amongst 5900 people who were elder than 65 years. In this case, the results showed that people who played golf had less history of strokes and heart attacks. But the government is not sure whether to consider golf as a legitimate exercise option to reduce health risks. Therefore, we will do hypothesis testing to see whether golf is a viable exercise option or not.

The null hypothesis is the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.

Here, the two populations will be that of golfers and non-golfers. The null hypothesis would mean that there is no difference in the rates of strokes and heart attacks in golfers and non-golfers.

Ho = Pg = Png

The alternative hypothesis would mean that the golfers have less chances of getting a stroke as compared to non-golfers.

H1 = Pg < Png

now, in this question, we do not have the data so as to do the test and solve for z-stat and p-value. Therefore, I'll just mention the test you can perform to solve this question. You can use the z-test for two proportions. I'll also give the formulas and criteria for rejection region.'

This tests for a difference in proportions. A two proportion z-test allows you to compare two proportions to see if they are the same.

• The null hypothesis (H0) for the test is that the proportions are the same.
• The alternate hypothesis (H1) is that the proportions are not the same.

You should have the values of both the proportions. And how many people are there in both the proportions. In this question, though we know the proportions for golfers and non-golfers with risk of heart attack. But, we do not know the exact split of the 5900 people into golfers and non-golfers.

This is how you calculate the z-stat.

Post that, you need to find the rejection region. This is region beyond which if the probability lies, you simply reject the null hypothesis.

Find the z-score associated with α/2. I’ll use the following table of known values:

Usually, α = 0.05(5%) for all statistical tests, unless mentioned otherwise. Thus, the z-value is 1.96 corresponding to the α value.

If the calculated z-stat from the formula is greater than 1.96, we reject the null hypothesis, otherwise we fail to reject the null hypothesis.