HYPOTHESIS TESTING Flashcards by Ady Cabalquinto

Method of making decision using data, whether from a controlled experiment or an observational study (not controlled)
Set of procedures that culminates in either rejection or non-rejection of null hypothesis

Hypothesis Testing
Involves the comparison of two hypotheses:
Null: Hypothesis of no difference & Alternative: w/ direction

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Correct Statistical Decision if:

p is greater than or equal to a

Reject null hypothesis

probability of occurrence of sample results is low

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Correct Statistical Decision if:

p is less than or equal to a

Do not reject null hypothesis

probability of occurrence of sample results is high

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probability of null hypothesis being true

p-value

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level of significance, cut-off value, tells whether the p-value is low or high

Alpha

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Identification: (Hypothesis Testing: One Proportion)

z = 
p = 
P =
n = 
Q =

computed z-value 
sample /statistical proportion
hypothesized population/parameter proportion
sample size
1-P

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TRUE OR FALSE:

Before proceeding, you must first check if sample size is nP > 5 and nQ > 5

TRUE

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A post EPI (expanded program on immunization) implementation survey was conducted among 200 randomly selected adults to determine if the aim of the MHO to cover 80% of the target population was attained. It was found out that 176 of the adults surveyed were immunized. Assume the MHO used a 95% confidence coefficient. Did the MHO meet his objective?

Ho :
Ha :

Ho: The proportion of immunized adults in the target population is equal to 0.80 or 80%

Ha: The proportion of immunized adults in the target population is not equal to 0.80 or 80%

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Are the assumptions met?
nP:
nQ:

Yes
nP= 160
(200x0.80)

nQ= 40
(1-P)(200)

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State level of significance:

a= 0.05

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Select test statistic:

z= p-P/√PQ/n

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Determine critical region:

z ≤ -1.96 or ≥1.96

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Compute test statistic:

z= 2.83

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Make a statistical decision:

Reject Ho

2.83 is not within the non-rejection area which is z ≤ -1.96 or ≥1.96

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Conclusion:

There is sufficient evidence to say that the proportion of immunized adults in the target proportion is not equal to 0.80 or 80%. It is significantly higher than 80%

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TRUE OR FALSE: Hypothesis Testing: One Proportion via OpenEpi

If target proportion is outside confidence limit (CL), H0 will be rejected, if hypothesized target population proportion falls w/in CL, do not reject H0

TRUE

TRUE OR FALSE: Hypothesis Testing: One Proportion via OpenEpi

p ≤ alpha: reject H0; p> alpha: do not reject H0

TRUE

2 Types Hypothesis Testing: (Two Proportions)

Random Selection

Random Allocation

A survey covered by the CPHM students in College of Medical Laboratory Science Department to determine the prevalence of hypertension in Marulas and Karuhatan, Valenzuela City was undertaken. Of the 414 respondents in Marulas, 46 were hypertensives as compared to 62 of the 410 respondents in Karuhatan. Do the prevalences of hypertension in the two barangays differ significantly? Assume 0.90 level of confidence.

Supply the missing items:
1. Ho:
   Ha:
2. a:
3. test statistic:
4. critical region:
5. compute test statistic
6. statistical decision:
7. conclusion:

Ho: The prevalence of hypertertension in Marulas is equal to the prevalence in Karuhatan.
Ha: The prevalence of hypertension in Marulas is not equal to the prevalence in Karuhatan
a: 0.10
test statistic: (formula of z test for 2 proportions)
critical region: z ≤ -1.64 or ≥1.64
compute test statistic: -1.71
statistical decision: reject Ho
(The computed Z of -1.71 is less than the critical value of 1.64 at a: 0.10)
conclusion: There is sufficient evidence to say that the prevalence of hypertension in Marulas is not equal to the prevalence in Karuhatan. In fact, the prevalence of Marulas is significantly lower than the prevalence in Karuhatan

TRUE OR FALSE
Hypothesis Testing: One Mean

The test statistic depends whether or not the population variance (σ2) or population SD (σ) is known, from literature or previous studies

TRUE
(If known: sampling distribution of mean is normally distributed; z-test
if unknown: sampling distribution of mean is t-distributed; t-test)

TRUE OR FALSE
Hypothesis Testing: One Mean

Deals with only one sample or group; Hypothesis is that the population mean is equal to a presumed/ hypothesized mean value; P = p or μ = x̄

TRUE
Null hypothesis: H0: 𝜇 = 𝜇0
Alternative hypothesis
H0: 𝜇 ≠𝜇0 (two-tailed, commonly used) 
H0: 𝜇 < 𝜇0 (one-tailed) 
H0: 𝜇 > 𝜇0 (one-tailed)

The average number of persons per household for the whole country based on the 1980 census results is 5.6. If a random sample of 25 households in a survey done lately showed a mean household size of 5.2 persons with a standard deviation of 1.56, does this result indicate that there has been a change in the mean household size in the Philippines since the last census? (use 𝛼 = 0.10; CL = 90%).

Supply the missing items:
1. Ho:
   Ha:
2. a:
3. test statistic:
4. critical region:
5. compute test statistic
6. statistical decision:
7. conclusion:

Ho: The mean household size in the Philippines is equal to 5.6
Ha: The mean household size in the Philippines is not equal to 5.6
a: 0.10
test statistic: (t-test)
critical region: t ≤ −1.711 𝒐𝒓 𝐭 ≥ 1.711
df = n-1: 25-1 = 24
t (0.10 (2-tailed), 24) = 1.711
compute test statistic: t= -1.28
statistical decision: not reject null hypothesis
(The computed t of -1.28 is not less than/ greater than the critical value of -1.711 at a= 0.10)
conclusion: There is no sufficient evidence to say that the mean household size in the Philippines is not equal to 5.6

TRUE OR FALSE
Hypothesis Testing: Difference of Two Sample Means

Research objectives often calls for a comparison of two groups/ samples; Used if the variables of interest (outcome/ dependent variable) is quantitative and measured using interval/ratio scale

TRUE

Considerations in choosing a test statistic when testing a hypothesis for two sample means:

Which test statistic is appropriate if:
Independent samples
Populations normal
Variances known

z-test (standard normal distribution)

Considerations in choosing a test statistic when testing a hypothesis for two sample means: Which test statistic is appropriate if: Independent samples Populations normal Unknown variances but assumed equal

t-test (t distribution with df)

Considerations in choosing a test statistic when testing a hypothesis for two sample means: Which test statistic is appropriate if: Related samples

t-test (t distribution with df)

Ways of Obtaining Two Independent Samples: Two independent samples randomly selected from two populations e.g. Males —> RS —> males Females —> RS —> females

``` Random selection (Randomly select from each population) ```

Ways of Obtaining Two Independent Samples: Two independent samples arising from random allocation to two groups e.g. Randomly allocate to two treatments

Random allocation

What are the two ways of obtaining two related samples?

Pre- and post- measurements | Match samples

TRUE OR FALSE: Z-test for two independent sample means; Formula is based on the sampling distribution of the difference between two means

TRUE

Suppose that the journal article reports that the mean age at marriage of Filipino women in urban areas is 22.6 years while those in rural areas is 18.4 years. These findings are based on a sample survey of 150 urban and 180 rural women. The report did not indicate the corresponding variances of the estimates. However, a review of past data shows that the variances for the age at marriage of Filipino women are 7.2 and 5.8 for urban and rural areas, respectively. Is there a significant difference between the age at marriage of women in urban and rural areas? Use alpha= 0.05; 95% CL ``` Supply the missing items: 1. Ho: Ha: 2. a: 3. test statistic: 4. critical region: 5. compute test statistic 6. statistical decision: 7. conclusion: ```

1. Ho: The mean marrying age of women in urban areas is equal to that of women in rural areas. Ha: The mean marrying age of women in urban areas is not equal to that of women in rural areas. 2. a: 0.05 3. test statistic: (z-test) 4. critical region: z ≤ -1.96 or ≥1.96 5. compute test statistic: z= 14.83 6. statistical decision: reject Ho (Since the computed value of Z = 14.83, falls within the critical region) 7. conclusion: There is a difference between the mean marrying age of women in urban and rural areas. (Women in rural areas tend to marry at a younger age than those in urban areas)

A research team collected serum amylase data from a sample of 15 healthy subjects whose mean is 120 unit/mL of an S.D. of 40 units/mL and from a sample of 16 hospitalized subjects with mean of 96 units and an S.D. of 35 units/ml. Are the researchers justified in concluding that the population means are different? Use alpha= 0.05. ``` Supply the missing items: 1. Ho: Ha: 2. a: 3. test statistic: 4. critical region: 5. compute test statistic 6. statistical decision: 7. conclusion: ```

1. Ho: The mean serum amylase of healthy individuals is equal to that of hospitalized individuals Ha: The mean serum amylase of healthy individuals is not equal to that of hospitalized individuals 2. a: 0.05 3. test statistic: t-test (t distribution with df) 4. critical region: t ≤ −2.045 𝒐𝒓 𝐭 ≥ 2.045 (df = n-2 = 31-2 = 29) t (0.05, 29) = 2.045 5. compute test statistic: 1.78 6. statistical decision: not reject Ho (The computed t of 1.781 is not greater/ less than the critical value of 2.045 at a= 0.05) 7. conclusion: There is a different bet the mean serum amylase of healthy individuals to that of hospitalized individuals. (The mean serum amylase of healthy individuals is significantly higher than those who are hospitalized.)

Hypothesis Testing: Two Means; 2-related samples It is claimed that the new diet will change a person’s weight in a period of 2 weeks. The weights of a random sample of 7 women who followed this diet were recorded before and after a 2-week period. Assume that the distribution of weights is approximately normal. Is there reason to believe that the claim is true? Use alpha: 0.05. ``` Supply the missing items: 1. Ho: Ha: 2. a: 3. test statistic: 4. critical region: 5. compute test statistic 6. statistical decision: 7. conclusion: ```

1. Ho: The mean difference in weight of women before and after the diet regimen is equal to 0 Ha: The mean difference in weight of women before and after the diet regimen is not equal to 0 2. a: 0.05 3. test statistic: t-test (t distribution with df) 4. critical region: t ≤ −2.447 𝒐𝒓 𝐭 ≥ 2.447 (df = n-1: 7-1 = 6 t (0.05,6) = 2.447) 5. compute test statistic: 0.015 or 0.01 6. statistical decision: The mean difference in the weight of women before and after the regimen is not equal to 0 7. conclusion: There is a significant reduction in the weight of women after undergoing the regimen