During the Covid crisis, there were lockdowns and working-from-home, which made collecting data on unemployment more challenging. Researchers from Heriot Watt University conducted a survey of 400 individuals in the labour force to assess rise in unemployment in September 2020. The object was to find out whether the unemployment rate had risen above a benchmark proportion of 6 per cent of the labour force in Malaysia. Of the surveyed persons, 34 reported being unemployed in the week prior to the survey.

The First Test Result (Two Test)

We have the given as follows: n = 400 X = 34 p = x = 0.085 hypothesized p = 0.06 Ho: The proportion of unemployment in the labour force in Malaysia is equal to 0.06 ; p = 0.06 Ha: The proportion of unemployment in the labour force in Malaysia is not equal to 0.06 ; p =/= 0.06 Significance level: Assume a significance level of 0.05 Test statistic: The z-statistic is computed as follows: p - Po Z po (1 - po) n 0.085 - 0.06 = 0.06(1 - 0.06) 400 = 2.105 Assumptions: 1. The data are simple random values from the population 2. Population follows a binomial distribution 3. When both mean (np) and variance( n(1-p)) values are greater than 10, the binomial distribution can be approximated by the normal distribution Source: https://sixsigmastudyguide.com/one-and-two-sample-proportion-hypothesis-tests/ Check np and nq: np = 400 * 0.085 = 34 nq = 400 * (1-0.085) = 366 Assumptions are satisfied.Hypothesis testing: Solution: The following information has been provided: Hypothesized Population Proportion (po) = 0.06 Favorable Cases (X) = 34 Sample Size (n) = 400 Sample Proportion (p) = 0.085 Significance Level (a) 0.05 (1) Null and Alternative Hypotheses The following null and alternative hypotheses for the population proportion needs to be tested Ho : p = 0.06 Ha : P # 0.06 This corresponds to a two-tailed test, for which a z-test for one population proportion will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a two-tailed test is z = 1.96. The rejection region for this two-tailed test is R = { z : (z| > 1.96}(Em The z~statistic is computed as follows: PPo po(1po) 12 0.085 0.06 [0.060 0.06) 400 = 2.105 mmmmwwm Since it is observed that lz| = 2.105 > of = 1.96, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p.va|ue is p = 0.0353, and since p = 0.0353