// Numbas version: exam_results_page_options {"name": "Simon's copy of Perform a t-test to decide if two sample means differ, ,", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": ["stats"], "advice": "

(a)

Test statistic

We should use the t statistic as the population variance is unknown.

This is an unpaired test so we must find the pooled standard deviation, as given by :

\\[s = \\sqrt{\\frac{\\var{n1 -1} \\times \\var{sd} ^ 2 + \\var{n2 -1} \\times \\var{sd1} ^ 2 }{\\var{n1} + \\var{n2} -2}} = \\var{tpsd} = \\var{psd}\\] to 3 decimal places.

The test statistic is given by \\[t = \\frac{|\\var{m} -\\var{m1}|}{s \\sqrt{\\frac{1}{ \\var{n1} }+\\frac{1}{ \\var{n2}}}} = \\var{tval}\\] to 3 decimal places.

(Using $s=\\var{tpsd}$ in this formula.)

(b)

p value range.

As the degree of freedom is $\\var{n1}+\\var{n2}-2=\\var{n-1}$ we use the $t_{\\var{n-1}}$ tables. We have the following data from the tables:

{table([['Critical Value',crit[0],crit[1],crit[2]]],['p value','10%','5%','1%'])}

We see that the $p$ value {pm[pval]}.

(c)

Conclusion

Hence there is {evi1[pval]} evidence against $\\operatorname{H}_0$ and so we {dothis} $\\operatorname{H}_0$.

{Correctc}.

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Link to use of t tables and p-values in Show steps.

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Step 1: Null hypothesis

If $\\mu_M$ is the mean for time spent by {things} and $\\mu_F$ is the mean for time spent by {things1} then you are given that:

$\\operatorname{H}_0\\;:\\;\\mu_M=\\mu_F$.

Step 2: Alternative Hypothesis

$\\operatorname{H}_1\\;:\\;\\mu_M \\neq \\mu_F$.

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Step 3: Test statistic

Should we use the z or t test statistic? Input z or t.

[[0]]

Now calculate the pooled standard deviation: [[1]]

Now calculate the absolute value of the test statistic = [[2]]

(Note that in this calculation you should use a value for the pooled standard deviation which is accurate to at least 5 decimal places and not the value you found to 3 decimal places above).

Step 4: p-value range

Use tables to find a range for your p -value.

Choose the correct range here for p : [[0]]

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Given the $p$ - value and the range you have found, what is the strength of evidence against the null hypothesis?

[[0]]

Your Decision about $H_0$:

[[1]]

Conclusion:

[[2]]

{this}

A random sample of $\\var{n1}$ {things} and $\\var{n2}$ {things1} gave the following results in {units}.

{table([['Male',{m},{sd}],['Female',{m1},{sd1}]],[' ','Mean','Standard deviation'])}

Perform an appropriate hypothesis test to see if there is any difference between {that} between {things} and {things1} (the null and alternative hypotheses have been set out for you).

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