Lecture 24- HT mean/prop

Question 1

What is the purpose of hypothesis testing?

Answer 1

• Used to assess the strength of evidence in our data against some claim.
• We need a systematic and objective way to determine this (otherwise everyone would have a different point at which they would disapprove a hypothesis).

Question 2

What is a null hypothesis?

Answer 2

A null hypothesis (H0) is generally the hypothesis that there is no
association, no effect or no difference

Question 3

What is an alternative hypothesis?

Answer 3

The alternative hypothesis (HA) is generally the hypothesis that
there is an association, effect or difference.

Question 4

What hypothesis (alternative or null) do we use as our working hypothesis while doing hypothesis tests?

Answer 4

The null hypothesis: it’s the same the same as court of law. We assume innocence until proven guilty. It’s not until we have gathered enough evidence that we reject the null and move towards the alternative hypothesis.

Question 5

Do we ever say that the alternative hypothesis is proven true?

Answer 5

No can never prove it only support cause we haven’t ruled out all other possible options.

Question 6

What are the general steps for hypothesis testing?

Answer 6

1. Set up the null hypothesis (H0) about the population
   parameter of interest - e.g. parameter = null value
2. Propose the alternative hypothesis (HA) - e.g. parameter ̸= null value.
3. Calculate the test statistic.
4. Calculate the p-value (probability of observing the test statistic from 3, or one more extreme, assuming the null hypothesis is true).
5. Interpret the p-value.

Question 7

What P value do we view as significant?

Answer 7

The P value is the probability of getting the P value or value more extreme is the null hypothesis stands true.

At p less than 0.05 we reject the null. This is saying that the value would be very unlikely (in the very tails) if the curve followed a T distribution with mean according to the null.

Question 8

How do you calculate a test hypothesis?

Answer 8

t-statistic, T = (observed sample value - null value)/ estimated standard error

i.e. the number of standard errors from the null value to the sample value.

Question 9

Calculate the T statistic for the Shoshoni rectangle example given…
x¯ = 0.6513 and s = 0.06655, with n = 18
the null value was 0.618

Then calculate and interpret the P value according to this…

Answer 9

2.122 (working on slide 455)

p-value based on t17 distribution is 2 Pr(T > 2.12) = 0.049
- in R: 2*pt(2.12,17,lower.tail=FALSE)

NOTE: have to times by 2 because there is 2.12 in both extremes

This p value is less than 0.05 therefore can reject null and go with the alternative hypothesis: there is a true difference in the Shoshoni triangles and golden triangle ratio.

Question 10

What is the significance level of P the same as?

Answer 10

The alpha level according to the confidence level calculated e.g. for 95% alpha is 0.05 (5%)

If alpha was 0.01 like when calculating 99% confidence interval then we have statisical significance at the 1% level.

Question 11

In a large overseas city it was estimated that 15% of girls between the
ages of 14 and 18 became pregnant. Parents and health workers
introduced an educational programme to change this percentage. After four years of the programme, in a random sample of 293 18-year-old girls, 27 had become pregnant.

Go through the process for hypothesis testing using this example…. (its the same but this time using proportions not means)

Answer 11

Work through answer from slide 462 to 465

Question 12

What’s an important difference when hypothesis testing for a proportion not mean?

Answer 12

• Use the equation for standard error from sampling proportion
• use pnorm when finding p value not pt