Question

A student pursuing a degree in English as a second language believes the proportion female factory workers who can't speak English is greater than the proportion of male factory workers who can't speak English. To test her claim she randomly selects 310 female factory workers and out of them 70 could not speak English. She then randomly selects 351 male factory workers and out of them 69 could not speak English. Test her claim at αα=0.05 to see if she was right. The correct hypotheses are:

• H0:pF≤pMH0:pF≤pM
  HA:pF>pMHA:pF>pM(claim)
• H0:pF≥pMH0:pF≥pM
  HA:pF<pMHA:pF<pM(claim)
• H0:pF=pMH0:pF=pM
  HA:pF≠pMHA:pF≠pM(claim)

Since the level of significance is 0.10 the critical value is 1.282

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

The decision can be made to:

• reject H0H0
• do not reject H0H0

The final conclusion is that:

• There is enough evidence to reject the claim that the proportion female factory workers who can't speak English is greater than the proportion of male factory workers who can't speak English.
• There is not enough evidence to reject the claim that the proportion female factory workers who can't speak English is greater than the proportion of male factory workers who can't speak English.
• There is enough evidence to support the claim that the proportion female factory workers who can't speak English is greater than the proportion of male factory workers who can't speak English.
• There is not enough evidence to support the claim that the proportion female factory workers who can't speak English is greater than the proportion of male factory workers who can't speak English.

Answer 1

The statistical software output for this problem is :

H0:pF≤pM
HA:pF>pM(claim)

Test statistics = 0.920

P-value = 0.179

There is not enough evidence to support the claim that the proportion female factory workers who can't speak English is greater than the proportion of male factory workers who can't speak English.