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Hypothesis Testing

Z-test for Proportion examples

  • STATISTICS
Z-Test for Proportion In this tutorial we will discuss some numerical examples on one sample Z test for testing population proportion. Example 1 An insurance company states that 90% of its claims are settled within 30 days. A consumer group selected a random sample of 75 of the company’s claims to test this statement. If the consumer group found that 55 of the claims were settled within 30 days, do they have sufficient reason to support their contention that fewer than 90% of the claims are settled within 30 days?
5 min Read 3

z-test for two means

  • STATISTICS
Two sample Z test for means In this tutorial we will discuss two sample Z test for testing the difference between means of two populations when the population standard deviations are known. In practice two sample Z test is not used often, because in reality the population standard deviations $\sigma_1$ and $\sigma_2$ are unknown. In such a situation, the sample standard deviations are used and two sample t test (Equal variances) or two sample t-test (Unequal variances) is used.
3 min Read 2

z-test for two proportions

  • STATISTICS
Two sample proportion test Suppose we want to compare two distinct populations $A$ and $B$ with respect to possessions of certain attribute among their members. Suppose take samples of sizes $n_1$ and $n_2$ from the population A and B respectively. Let $X_1$ and $X_2$ be the observed number of successes i.e., number of units possessing the attributes, from the two samples respectively. Then, $\hat{p}_1=\frac{X_1}{n_1}$ be the observed proportion of successes in the sample from population $A$.
3 min Read 2

z-test for two proportions examples

  • STATISTICS
$Z$-Test for difference of Proportions In this tutorial we will discuss some numerical examples on two sample Z test for proportions using traditional approach and p value approach. Example 1 A survey indicate that of 900 women randomly sampled, 345 use smartphones. For the men, 450 of the 1025 who were randomly sampled use smartphones. Test whether a percentage of women who uses smartphone is less than men. Use $\alpha=0.05$.
6 min Read 4