confusion re: null hypothesis for population mean test

Hi everyone, please could someone tell me which is the null hypothesis in the question below? I find the wording confusing.

"For the case of a known population standard deviation =2, test the
hypothesis that the population mean is larger than 49.15 against the alternative hypothesis that it is equal to 49.15, using a confidence level of 99%"

I am confused because the question refers to the alternative hypothesis being equal to 49.15, while every worked example I have seen shows that it's the null hypothesis that is set to be equal to a specific value. Can the null hypothesis be Ho>49.15 and H1=49.15, or should I ignore the wording in the question and set the null hypothesis to be Ho=49.15?

If the null hypothesis is Ho>49.15 (rather than =49.15), would we still reject it if Z exceeds the critical value?

Thank you in advance for any explanations you may be able to share!

Reply 1

mqb2766

Original post by beabramble

Hi everyone, please could someone tell me which is the null hypothesis in the question below? I find the wording confusing.
"For the case of a known population standard deviation =2, test the
hypothesis that the population mean is larger than 49.15 against the alternative hypothesis that it is equal to 49.15, using a confidence level of 99%"
I am confused because the question refers to the alternative hypothesis being equal to 49.15, while every worked example I have seen shows that it's the null hypothesis that is set to be equal to a specific value. Can the null hypothesis be Ho>49.15 and H1=49.15, or should I ignore the wording in the question and set the null hypothesis to be Ho=49.15?
If the null hypothesis is Ho>49.15 (rather than =49.15), would we still reject it if Z exceeds the critical value?
Thank you in advance for any explanations you may be able to share!

where is the question from/do you have the ans? Id agee the null/alternative should be the other way round, Treating it as a z, then sigma/4 =1/2 so the score 1.7 is well away from the 99% boundary, so much so that it sounds wrong.