oh yh forgot to add them

"Sprinters produce packets of crisps, some of which contain a prize voucher. Jean wishes to test whether the proportion of packets with a voucher is in fact 1/5.
1) State the null and alternative hypothesis

Jean buys 12 packets and finds no vouchers at all

2) carry out the hypothesis test at a 5% significance level, giving the critical region for the test and stating your conclusions.
3) how many packets of crisps would Jean have to buy for the critical region to have a non-empty lower tail?"

Many thanks

Reply 3

RickHendricks

19

Original post by cparish3nty

1.

oh yh forgot to add them

"Sprinters produce packets of crisps, some of which contain a prize voucher. Jean wishes to test whether the proportion of packets with a voucher is in fact 1/5.
1) State the null and alternative hypothesis

Jean buys 12 packets and finds no vouchers at all

2) carry out the hypothesis test at a 5% significance level, giving the critical region for the test and stating your conclusions.
3) how many packets of crisps would Jean have to buy for the critical region to have a non-empty lower tail?"

Many thanks

You should understand that:
The null hypothesis is the hypothesis made by the RESEARCHER, which they are trying to discredit or disprove.
The alternate hypothesis is the one that the researcher is trying to prove it true.

For example, if someone tells me that the probability of it raining today is 0.5, and I think it's higher than that, so I go ahead and try it out,

the null hypothesis in this instance is that the probability of it raining today is 0.5,
and the alternate hypothesis is that the probability of it raining today greater than 0.5

You can represent this numerically by having

\mathbf{h_0}:\mathbf{p}=0.5

and

\mathbf{h_1}:\mathbf{p}>0.5

Where

\mathbf{h_0}

is the null hypothesis and

\mathbf{h_1}

is the alternate hypothesis.

Go ahead and use the information I've given you to do the first question.

The 2nd question is standard, so I want you to attempt it, or begin it first, and I'll help you if you need help.

Original post by cparish3nty

1.

oh yh forgot to add them

"Sprinters produce packets of crisps, some of which contain a prize voucher. Jean wishes to test whether the proportion of packets with a voucher is in fact 1/5.
1) State the null and alternative hypothesis

Jean buys 12 packets and finds no vouchers at all

2) carry out the hypothesis test at a 5% significance level, giving the critical region for the test and stating your conclusions.
3) how many packets of crisps would Jean have to buy for the critical region to have a non-empty lower tail?"

Many thanks

Have you tried anything?

The null hypothesis is our current belief, which is that the proportion of packets with a voucher is 1/5. (that is, the probability of getting a voucher from randomly picking a packet is 1/5)

The alternative hypothesis is essentially the "opposite" to the null hypothesis. It's what we accept if we reject the null hypothesis. In our case, it's that the proportion of the packets with a voucher is not 1/5. (note that this is a two tailed test)

Hypothesis Testing

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